You bet your A-- it will work!
I know this will stirr up a hornets nest, but I have seen the .223 Remington take many whitetails, a few, out to 300 yards!
You said it properly, shot placement is the key!
I have only used 55 grain bullets!
If you put one tight behind the shoulder, that deer will not go far! Many times, if they are not "alert", they will drop right there! If you're worried about the deer running across the property line after the shot, etc, your best point of aim would be centered with the front leg, about 8 inches down from the top of the shoulder! If you hit there, the deer will drop in it's tracks!
NOTE:
I have shot deer with my 221 fireball and also with my 22 Hornet! The bullets of choice were 221 FB, 50 grain Hornady sp and, 22 Hornet, 45 grain Hornady sp! All shots were through the ribs except for one time with the Hornet, I put it high on the shoulder (at about 75 yards) and he dropped right there. I never had one move over 2 or 3 steps!