Egg Replacer

My friend recently bought me a box of this egg replacer. I'm not a vegan, so I'm basically using it as a back-up when I don't have any eggs lying around (I do a lot of quick bread baking, so it comes in handy for cookies and the like).

I was wondering, though, how well this would work for breads. Egg is often used in bread as a softener, a source of fat, and for flavor, right? The replacer is really meant to emulate the chemical qualities of egg (that is, it's leavening abilities for things like cookies), so would it work well for yeasted breads? I especially wonder about breads like brioche, challah, and pain au lait where the egg flavor/fat would seem to be central. I know that there are some vegan recipes for these out there using egg replacer, but I wonder if you can just take any ol' bricohe recipe and substitute the replacer in.

I was also wondering if egg replacer would work well for egg washes.

Any thoughts?