Yes, you will likely have to raze a few cities along the way when doing a conquest/domination, that is one reason why a diplo win can really complicate these types of multile way wins. However, you may make those types of moves at the end of the turn and then chose to abandon cities (not that it saves rep) that don't add to your needs.
When you add culture into the mix sometimes you have to destroy cultural buildings just before they expand city borders, like when a ciy has 99 culture, it's cultural expansion (when to it hits 100) could throw you over the domination threshold.
In GOTM15 I had to destroy quite a lot of cultural buildings to hold off the culture win to 1585AD, if I would have been smart I would have kept scientific "pet civs" and could have cut about 12 turns off my game, oh well. I think if I had done just a straight culture win it would have been before 1500AD, kind of like GOTM14.