Will a developer fix a (small) broken mechanic, or should I fix it before the submission process begins?
You should fix it before submitting the game.

The developer will have plenty of work to do anyway, from working on issues you're not even aware of, to tweaking factors to bring the game closer into line with the publisher's target audience. The better your game is before you submit it, the more likely that first play will be fun enough to make the publisher take interest.