This depends on the school where the WL opportunity came up. For many, it will be early enough in the process that nothing will be different, and many schools go to lengths to make sure this is the case. For others, it could be tough in term of housing or even course selections. You’ll usually know which these are, btw, as the strategies for housing, roommates, etc are no secret among students there.
I have one friend whose S got in so late in the process that he ended up in a house for an affinity group where he was the only person not of that affinity group. (This is, btw, the only time I have heard of this, but his description was “yeah, I got someone else’s place – literally! – when they bailed”. Fwiw, they all got along great and remain friends.)
This is why kids who are so tied up in the WL process in May end up passing up offers later in the summer. The “trade up” often has to be significant to start unwinding exciting plans.