Too much stuff in play. More than half of all abortions in the U.S. are by drugs, not surgery. It'll have to shake out which states will ban the drugs, and how the Federal government (which has authority over the postal system) rules on mailing the drugs into banning states.
Further, unless the people with WAAAY too much interest in what's going on in other folks' pants get their way and pass a national ban, abortion'll never be more'n a few states away. If you can afford a visit from a travelling abortionist, you can afford a bus ticket from Houston to Las Cruces, New Mexico. Or Ciudad Acuna, Old Mexico.
The only real effect these bans will have (besides letting the self-righteous get all puffed up) will be to ensure that those who are least able to care for a child will be the most likely to have them.