After my last trip, I had a little water drip from the hose into the gutter. It pooled and dried in the gutter and never dripped out into the door compartment, though...I think I'd rather keep it in the gutter that I already consider soiled anyway than let it drip out anywhere else. Since I always wear gloves when I pull the gutter out to get the hose, that's a good place to keep any water that doesn't dry from the hose before I put it away.
It should be mostly gray water anyway, for what that's worth.