Folks... right now i'm going to say it is VERY possible!! However, unlikely.
Being a "hands on" kind of guy, I set up a very crude test of my own. I have an old deer hide, tanned hair on, and draped it over an empty one gallon plastic milk jug. Using a Crossman 2100 Classic .177 caliber air rifle (pumped 5 times, MV unknown) at a range of +/- 50 feet, put 5 out of 5 bb's through the hide and into the milk jug. All the bb's were captured inside the jug with no pass throughs. At ten pumps, the rifle's advertised max, the next five shots were complete pass throughs, hide and jug, and into the dirt.
My personal conclusion... "Possible" if using a rifle with more power than a Red Ryder. "Unlikely" due to all the variables that would have to fall neatly into place. "Doubtful" that even if penetration to the heart is possible, that the deer would pile up so quickly.
I'll be happy to do more testing if anyone would like to offer more "control" variables I should try... Not to mention another milk jug...