Nope.
Since the AE86 is a Front Engine/Rear Wheel Drive setup it's not going to work in a Mid-Engine/Rear Wheel Drive setup.
One of the problems with Mid/Rears is the limited availability of Engine Swaps.
I know people have swapped other motors into the First Gen's but I'm not sure if they were one off's or if there's a popular option. Check out a good MR2 Forum.
http://mr2.com/forums/
I'm sure there's a few people who have done swaps and can give you a better idea of what's involved.