How can I change the animation for a dropped object (turret) to that of a thrown object (grenade)? I still want to have the dropped object animation for dropped items.

In some force powers it gives you a line where it says what animation to use. You can copy that line into your odf for the auto turret and then change it to whatever the animation for a grenade is.

I've found that dispensers in the common side often have this line commented in their odfs.
I don't know much about calling animations, but you could try uncommenting the line to see if it does anything. It is included in the autoturret's (parent) odf.

That should work and to be safe copy and uncomment the line in the child's odf.

Nope, tried that, that animationbank doesn't exist.

I beleive that Syth was able to change the grenade animation in his BF2 mod. Its pretty much the same principle, so you could ask him on it.

Better yet, try changing the dispenser's classlabel to grenade. Dispensers and grenades don't specify any animations AFAIK, so it's likely a hardcoded association.