Apparently I have never made traditional Polish beet kvass because I have never made it with a slice of dried rye bread.
I assume they used the bread to introduce micro-organisms, and maybe provide easily digestible surgars like you said. But beets have plenty of simple sugars in them anyway. So, I honestly don't know.
Anyway, you can do with out. I make beet kvass all the time, it nearly always turns out delicious, and I never use the bread. Just chop beets, and some salt, add some water, and wait a few days.