Maybe. But so far their damage has held over from one episode to the next unless there was a week or so between episodes. And most of that was just hull repairs rather than critical systems.
We'll see later how messed up Yamato gets, and what it takes to fix her. I think they said she'd get altered during the trip due to damage.
Well, as they say:
It ain't really "Yamato" until the Third Bridge blows up and Yuki dies.