A bow wave will, yes, push water away but its main help is causing a trough in the engine bay which helps to keep water out of the electrical/air intake components. If the depth of the water is up to grill level and you can get the speed right it will lower the water level in the engine compartment considerably.
The main problem when wading through deeper water especially small lighter cars is traction. If the water is really deep usually the back end will start to float first, then the driver will back off the driver then loses momentum, engine bay then floods.