It depends. If the law says "you must perform such-and-such steps to verify age" then no, they don't care if you can counter it. If the law says "you must use an approach that is at least x% effective" then yes they do care if enough people counter it.

We already had a half-assed solution, where websites would require you to press the button that says "I am over 18". Clearly somebody decided that wasn't good enough. That person is not going to stop until good enough is achieved.