Not if you have ears. The accent changes almost immediately.
At some crossings, yes. Between Detroit and Windsor you will hear it, largely because of the big black American population on the Detroit side. Anywhere on the Quebec border, yes, since there will usually be more English-speaking people on the US side and French-speaking people on the Quebec side. I'm most likely to cross between Washington State and BC, where Vancouver and Interstate 5 are. There, the only major difference I notice is that there are more Asians on the Canadian side of the border, as you're already in Vancouver when you enter Canada at that crossing, whereas the Washington side is predominantly white American, so in that sense, I might hear a different accent.
But the differences in accent when you cross the border are nothing compared to the difference you hear going coast to coast within either country. If you're from Vancouver, you will hear bigger differences in accent going to Quebec or Atlantic Canada than you would crossing into Washington State. Likewise, if you're from Seattle or Bellingham, you will hear bigger differences in accent going to Hawaii, the southern states, or New York than when you cross into the Vancouver area.
In fact, a lot of Americans are very much aware of the rest of the world as a whole.
But, many are not really aware that Canada is significantly different than the US. There is a tendency to think of Canada as "USA Lite", if they think of the country at all.
The reality is, for most citizens of the USA, Canada is largely irrelevant. It has a population that is roughly the same as California, spread over lands that are even larger than the USA. Canada is NOT a world power, it is largely economically dependent on the US for most of its markets, and it's military is miniscule. Its inhabitants are not constantly sneaking into the country illegally (even though my own father did exactly that).
Frankly, there is little reason for most people in the US to even think about Canada. That is sad, but it is fact.
I was aware that Canada was different from the earliest age i can remember. I began spending summers in Canada in 1946 when I was 3), and I noticed that things were slightly different there. People tended to be a bit more formal, The King was on the currency, the flag was very different, the gas mileage was MUCH better than it was in the US (I didn't realize that the Imperial gallon was 5 quarts until I was a teen), etc.
But, my neighbors never really understood that i was spending the summer in a "foreign" country. I was going north, to be with Grandfather and my step-grandmother, and it was as if I was going to Washington (we were from Oregon).
Canada has VERY little impact on the lives of most Americans. Even Great Britain has a larger impact, as do most European countries. After all, most of your manufactured goods are exactly the same as they are here (even the same brands in most cases), you use the same measurements for most things, so what's to distinguish your goods from ours?
Now, if Canada had developed their own automobiles, and we were importing the "Montreal" car, people would notice. Or, if you had distinctive clothing, like Scotland has the kilt; or a radically different society, people would notice. But, in many ways, Canadians act much like their American cousins, your culture is not ad radically different as say between South Carolina and Vermont, you largely speak the same language, etc., etc., etc.
Back when there were wars between the two areas, Canada was NOT a country, it was simply a part of Great Britain (or as most Americans thought of it, a part of England). The USA has never fought with Canada, it fought the Brits (and more than a few Canadians sided with the Americans, both in the American Revolution and in the war of 1812. Britain had to post a LOT of troops in Nova Scotia and New Brunswick, to keep them from joining the Americans.
So, even though our histories are intertwined in many ways, the vast majority of Americans just don't really think about Canada as being separate. Canada is just kind of thought of as another US State, sitting way up north.
If my dad's brother and his family hadn't moved to Vancouver when I was a pre-teen, I would have had little reason to think about Canada either. The rest of my dad's family was in California, other than one brother who never left the Philippines, so my uncle who ended up moving to Vancouver had other options at first. He would have liked to be in California with the rest of us. If that had been the case, the only people I would have known anywhere in Canada are distant relatives who are nice, but I wouldn't have gone all the way to Canada just to see them on a regular basis.
Apparently, my uncle's wife also had Alberta and PEI as options in getting work before they migrated. I've been to Alberta a few times in my 20s, and I can kinda appreciate it now, but I wouldn't have appreciated it so much in my teens. I went to PEI once a few years ago, and I didn't care for it. And I travel a lot and appreciate different places, so it's not like I close my mind that much.
If my relatives had moved to Alberta, I would have had less reason to put Canada on my radar. Even less if they had moved to PEI.
No offense to people from PEI, it just wasn't my kind of place. The same way that Vancouver isn't for everyone.
I know their lives would have been different if they had moved to PEI. They're Asian, like me, and being in Vancouver, most of their friends are Asian as well. Being in PEI, that would not be the case at all. In Alberta, it would be less the case than in Vancouver, but more than in PEI.
Anyways, my point is that after they moved to Vancouver, I went there regularly because my cousins there are roughly my age. At first, I felt attached to them, but I kinda grew apart from them as our interests and values evolved over the years.
Yet still, there was something I loved (and still love) about Vancouver that kept me coming back. Even if one of those cousins was someone I didn't get along with. I just really love Vancouver. To be honest, it does feel like a trip overseas. And growing as a teenagers conscious about their cultural background, Vancouver just seemed to be a place to connect to in ways that Calgary or Edmonton would not have fulfilled as much, and PEI not at all.
From that, I became curious about the rest of Canada and wanted to know more about the country in general. So I traveled to other places in Canada and learned more about the history. I'm not disappointed, though I like some things better than others.
But again, if my relatives hadn't moved to Vancouver, would Canada be on my radar? Probably not, but Mexico and the Philippines would be. In California, when you talk about "the border," which one do you think we're thinking. Does the Canadian border get 10,000 illegal crossings every day? Do you think the amount of smuggling between the US and Canada even begins to compare to what enters the US from Mexico?
Anyways, about the differences between Canada and the USA, I find that they are mostly either political or ethnic/regional. Quebec and Newfoundland are unique to Canada, whereas Canada didn't have much slavery, doesn't have Mexico for a neighbour, and doesn't have territories/provinces like Hawaii, Puerto Rico, American Samoa, or Guam, so the black Americans, Mexicans, Puerto Ricans, and Pacific Islanders provide a cultural dimension to American life that isn't prevalent in Canada.
I notice all the Asians in Vancouver, and that does remind me of California. However, the lack of blacks, Hispanics, and Pacific Islanders in Vancouver (or in Canada in general, other than small communities in Toronto and Montreal) is a HUGE difference that I notice. That's probably the biggest difference I notice, BY FAR!