Depends on where the constraint is. If you have tons of back strength and are limited by your overhand grip, you'll pull more. If grip isn't the issue and it's the main pull, you'll pull probably won't pull any more at all.
I will say though that you need to get used to a mixed grip before you go hoisting heavy weight with it. Personally I don't like them due to obvious factors like the lift not being as linear or potentially introducing rotation as wll as making a biceps tear more likely. But yeah, obviously I've used the mixed grip a lot over the years anyway. Got away from it when I was training with friends who were big into OL, if they trained the dead which wasn't typical they'd use straps or hook and pull overhand. Plus, you don't train mixed for a while and you really realize how odd it can feel not having that symmetry.
So there are some possible issues with mixed grip. To minimize this, you work on it with light weight to make sure all is kosher and gradually work up. If you are used to pulling overhand and have never done it, it's a significant alteration in the pull and can even affect your setup to a degree. Once you have been doing it for a while it's second nature though.