Quite so, many would still continue singing the current anthem. But people will be free to experiment, and slowly the current anthem will probably replaced by a more suitable one.
As to singing it at the Olympics, let the gold medalist choose which version he/she wants sung.
Actually, I just remembered that to a certain degree it's like that already. For example, at any given event, the event organizer must make a choice between the official French version, the official English version, or any of various possible combinations of the two.
Looking at it that way, seeing that they're faced with having to make such decisions already anyway, de-officializing the anthem isn't going to make things any more complicated than it is now. Just as they are forced to make a decision between various options now, so the same would apply by de-officializing the anthem, except that the options avaiable would be wider.