It can, if everything is perfect.. The old saying is shoot the most poundage you can handle and that will vary depending on if the bow really fits you..
It has plenty of power to kill a deer but you must do your part. Learn to gauge distance and shoot accurately within an acceptable range. I shoot a 40# bow and mine is a killer at ranges out to 20 yards. I won't shoot beyond that distance, +/- a yard or two.
I ran into the below information on some website years ago but I have learned to take them with a grain of salt as I think the bottom table maybe geared more towards compounds. Using a 45#@28" Hoyt Satori 19" riser ILF bow running a 539 grain arrow at 180 fps with 20.3% FOC I get a KE of 38.79. My friend runs the exact same setup and has had passthroughs on (2) elk between 20 and 24 yards. He has also taken several black bear with the same setup. Kinetic Energy = arrow velocity squared x mass weight of the arrow / 450240 KE = (180 x 180 x 539)/450240 = 38.79 KE Hunting Usage < 25 ft. lbs. Small Game 25-41 ft. lbs. Medium Game (deer, antelope, etc.) 42-65 ft. lbs. Large Game (elk, black bear, wild boar, etc.) > 65 ft. lbs. Toughest Game (Cape Buffalo, Grizzly, etc.)
Robert, you're probably correct with the formulas but I hunt with all wood bows and none of them will shoot 180 FPS. That's jet fast for a recurve. I don't shoot much over 40# though so who knows?
I took my first bow buck with a 45# recurve at 20 yrds. Here are two things to remember 1. IMO...good quartering away, faraway from shoulder bone shots 2. Understand they are slow. Your arrow will not have the speed of a compound. The ability of a deer to drop at shot thus increases. Deer with head up drops less.
I agree about the wood bows, my ILF bow is much faster then my wood bows. I have not put my Bear Cheyenne through the chronograph yet as I am still tweaking arrows for that bow. The Cheyenne is appears to be pretty quick. My Southwest Archery 40# Recurve is running 157 FPS with a ~10 GPI arrow, My Bear Kodiak Hunter is running at ~163 FPS with an ~10 GPI arrow. All Arrows are in the 18% to 20% FOC range. I do have some friends with some high-end custom bows that are really fast and easily passing 180 fps. (I don't know their arrow weights etc.. they were shooting that day).
One of my go-to bows is a 52" 40# @ 28" Toelke Kestrel. Dan doesn't make that bow any longer but when he did build it he superseded it with a similar bow he called a Troll. There is a guy on YT who does a test on a Troll, 40@28, etc., and using a light arrow, probably under 10 gpi he was able to shoot a couple of arrows at around 180-182. You might want to check that vid. Arrow speed is important but I'm not one who goes through the process of weighing each hunting arrow with its broad head and wondering, or working to determine, how fast it shoots. All I really care about is a quiet bow and accuracy because I know that with those two things I'll very likely take my deer.