Dropping it into gear will destroy any normal car transmisson. Manual or automatic, it dosn't matter. It fucks up automatics more because of how the gears work.
Now, if you take a turn really hard and just stomp the gas and the rear wheels start spinning like nuts, That's not too bad on the driveline. (more bad for the suspinsion being thrown around in directions other than up and down) Just try not to go over different surfaces that have varying ammounts of friction while the wheels are spinning. (like from water to dry pavement - that puts a lot of instantanious stress on the whole car)
You NEED an LSD (limited slip differential) to do this. If you do not know if you have one, odds are you do NOT (you would have an Open differential). Open diffs are really easy to tear up since the inner gears are so small and when they start spinning really fast (IE: when one wheel is still and the other is spinning like crazy) they can get a little jittery or something and they just chew themselves to pieces. Even the most basic LSD prevents this from happening by reducing the amount of wheel speed difference between the two wheels.
My buddy did doughnuts in the dirt in his truck a lot. His diff gears were ground SMOOTH. ZERO teeth. (they wern't broken off, it looked like the teeth were polished off) ...So be careful. (Since he had a chevvy, LSD's were cheeper than a BMW LSD. he probably only paid 1,000 to have a brand new 'positraction' diff put in, whereas I'd have to pay 2,000 just for the differentail)