If the load is a motor it's winding inductance will act as a filter to suppress the 15kHz component of the winding current.
As for whether the circuit will work properly, you still haven't specified the load. Any load with an inductive property may well need RC snubbers or other spike-suppression components to prevent damage to the FETS arising from back-emf effects. You may need to experiment. I suggest you google for typical H-bridge protection arrangements.