Disease causing microorganisms such as bacteria from your black tank can wiggle their way right back to the filter, does it protect you from water born pathogens? Probably not, hence the reason RV manufacturers don't connect the two systems. Get a different colored decicated water supply hose for the black tank and dry it completely between uses, or have a good supply of antibiotics on hand.
From what I understand of how the blank tank flushes work, I would think the chance of anything getting back into the sprayer from the tank are pretty small. Especially if you follow the suggest directions of draining the tank and keeping the dump valve open while using the sprayer.