United does not appear to do that by movement throughout the cabin. On the Business Class TATL that I flew with them this summer, they went front to back each direction but asked each person for their first choice and second choice (out of only three!). I presume whatever status-based priority they give, they do that "behind the scenes" (in the galley area, after they've collected everyone's choices) in resolving who gets first choice vs who gets second choice.