Felt recoil is Impulse which is the force (not energy) integrated over time
So no, but it is proportional. Regarding handguns, what further complicates things is that the force is not directly into the hand so there's an upward component (barrel flip) and a horizontal component that the palm captures.
Also, don't forget "felt" recoil is subjective. E. g. Locking my elbows increases my "felt" recoil because I'm stopping the gun faster (smaller delta t)