At a 35″ cabinet height with no toe kick, the cabinet case will sit directly on the floor. You will still need some type of build-up beneath the cabinet to raise the trash pullout front off the flooring so it can operate properly without rubbing.

A more typical height for a no toe kick cabinet is around 30.5″, as the cabinet height needs to be reduced to account for whatever platform or build-up you use. Below is a side view of the taller 35″ trash bin pullout cabinet for reference.

I would also highly recommend keeping your island cabinets around a 35″ total finished cabinet case height after the build-up to avoid ending up with an excessively tall island.