No doubt that a 22 wont
always do the trick. I even have a buckthat proves it. I shot an arcehry buck back in 2000 that had a big old wart under his eye. The taxidermist later told me he found a 22 slug embedded there that had healed over and calcified.
I will admit however, that poaching deer, whether with a crossbow or a 22 or a 30-06 is not my field of expertise.