test a transmission out of the car?

I saw a video on Youtube where they hooked a drill to the input shaft and spun it while shifting the transmission through the gears and watched the tailshaft for movement.Is that possible to do or would it damage the transmission?

If someone took the time to fabricate a proper pump-drive to go with that, and looped the oil lines, then yes it could be done. But it would only tell you that the circuits are working...or not. The clutches etc, could still be almost trash, and as soon as you put a load on the output-shaft, they could slip. But as already said; it would take a heck of a drill,not a fractional horsepower, and generally a drill that big is geared pretty slow. To be useful, I think you would need a brake on the back, and probably a 20hp electric motor, and a fluid coupling.
I worked at a transmission overhauling place in the 80s, and we had a 302Ford engine as a power unit. That thing ran almost from morning to night, testing every P-car and light-truck transmission the guys on the auto-line built. We had extremely few warranties. I think there were 4 or 5 guys on that line. I was the guy cramming out standards, all by myself, until they found out I could do more. Then they fired bigger and bigger stuff at me, and hired two guys to do what I had been doing. During my stay there, they doubled the business twice in about 4years, then built a huge complex; at which I only stayed about a year and a half. My favorite transmissions to build were RoadRangers which came in highway tractors; they gave me quite a workout. In between, I built rear-ends, alongside another guy.They moved me along fairly quickly after I became proficient at reading and adjusting patterns. All in all, that was a fun part of my life. Eventually I was building power-shifts and such, transmissions almost big enough to stand inside. That was fun,
and then I quit. It was time to make babies, and get out of the big city. That was 83/84 and our capitol was becoming a dangerous place to be. Sometimes I miss that line of work. And sometimes I miss the constant roar of that mighty test-mule 302.