Sure it would, but has some limitiations. Even though the 44 is a big badass cartridge in a revolver, it doesn't even carry as much punch as a 30-30 out of a rifle. So treat it like what it is - a handgun cartridge. Can it take deer? Of course, but keep the range sensible and the shots reasonable (no texas heartshots).
Keep in mind that this is essentially a higher-pressure version of the old 44-40, a cartridge that's (possibly) taken more deer than any other