It's certainly possible for it to cause an oil spill if you caused enough damage to the transmission. Can you reverse the car? If you can reverse the car then you probably didn't completely break the gear off. If it does reverse, does it feel lump or does it make unusual noises? If so then you might have damaged it, shorn off some teeth, etc. Do you have an automatic car? Some automatic cars protect you from this sort of thing.

Calvin