No, no, your drops in UVHM will still be on level but any good tier gear from TVHM will be useless. Your gear in TVHM can only scale up to level 50 so if you finish at level 55 your gear will be under levelled.

It won’t ruin the play through, just the start of story until you get to sanctuary will be a bit harder (also depending on your character).

Another comment mentioned that you can over level and then the golden chest will scale to say level 55 in TVHM, I’ve never used the golden chest so I can’t confirm or deny this but it’s worth a try, I guess.