Yes, it can happen. I've shot two deer at close range that did not react to the shot/shot noise.

Onedoe (after a heart shot with visible exsanguination) stood for just seconds, looking alertly at the rest of the herd alarmed by the noise --she fellin situand then the herd took off. There were 17 deer around me at the time.

Another doe (liver/lung) had abuck following her just a few feet away. At the shot, she just looked back at the buck as if to say "WTF?" and walked just a bit further before hip swaying and going down. The buck (nice 8ptr) tried having his way with her even after she had collapsed on the ground. The buck did not leave her as he watched me climb down my tree (hand climber)... it made me a bit nervous when he stood his ground, but he reluctantly departed and I claimed my prize.

-fsh