All things being equal, the answer is "NO". The lighter arrow just doesn't carry as much momentum to the target.

OMHO though, if you are hunting critters the size of deer the worry about Kinetic Energy, Momentum, and such just gets too much press. Years ago (many years) we shot bows that produced speeds of 180-190fps. We picked an aluminum arrow that spined and tuned right, shot them for target and hunting using a good sharp broadhead and shot right through deer. No problem. We didn;t worry about how much energy was produced or anything else. We learned to shoot the bow. That is what produced meat-on-the-table.

Man, guys are getting complete passthroughs on game as big as elk with 55lb recurves---still.