20 Inch Rear wheel on a 26 inch bike?

Pedals might bottom out unless you used a set of short cranks off a 20" cruiser or a16" kids bike making it difficult for an adult to pedal... adding a 20" wheel in the back will lower the bike by 3" so you can measure this part and see how much clearance you got...
Acceleration would be nice but top speed would suffer unless you used a very small sprocket.
The way it handles may suffer the most tho because the fork's rake angle will be changed considerably... changing the rake and trail wiill definitely change the way it rides and could cost some stability so proceed with caution here...
is there a specific reason you want such a small rear wheel? A lot of people have used a 24" wheel on the rear successfully so that might be a better option unless you're looking for a certain look for your build...

Usually a very bad idea. Makes pedal clearance a nightmare and also makes handling very twitchy due to trail changes sometimes. (Depends what fork you use)
Better off to mod a 20" frame than to stick 20's on a 26" frame in my opinion.

the 20" rear wheel will.work just fine and it will still handle fine, a 20" on the front is where the handling issues begin because it git very touch and will cut side to side quickly.

pedals off a 20 or 24" bike should give you all the ground clearan e needed and you can use a 28T sprocket on the rear wheel to keep a decent gear ratio, a 40+T on the rear and it will be a low speed hill limber that might even go up a wall.....lol!

to know what you have for sure its very easy to put the 20 wheel on the i tended crame and heck all the points of concern out.

Ive had 20" wheels on the larger frames andthey a tually handle better than on the 20" frames, the straight line balance is more stable because of the longer wheel base, when you shorten the wheel base is when they get more sensitive and will respond quicker to the bars being turned a little.

Ipersonally do like a 24" wheel on a 26 bike for the rear or even on the front also, lower center of gravity and the bike handles better.

give it a whirl, you may like it if you can get the gearing like you want.

I like a 24" rear with a fat tire like a 1.75 to 2.0 and a 26 up front with a fatter tire like a 2.35 or 2.5 for good handling... back in my bmx days I always ran a 1.75" rear and a 2.125" front for best handling since I wanted the bike to kick out the rear tire before the front, there was still plenty enough traction but the bike would corner a lot quicker and better with just the slightest bit more grip up front and I was always in better control if the rear would lose grip before the front in a really tight turn on the dirt... this might work a little different tho on pavement

youll need to measure your cranks if they're to long with a 20" rear wheel and then look into replacing themif yours are one piece thats an easy thing to do.

http://www.bicycledesigner.com/bike-parts/bicycle-cranks/1-piece-cranks-1.html

Very true on the cranks... you need the basic ground clearance but a little more to prevent road contact if pedaling in a turn. The 20" wheel will lower the back of the bike 3" but if the cranks are about in the middle of the wheelbase they may only drop about 1 1/2" or so, but the further back from the middle of the wheelbase the more they will drop with the smaller rear wheel. A set of short cranks can be taken from a 20" bike to give more ground clearance but these will also offer less leverage and be slightly more awkward to pedal if you're used to the regular long cranks.
You can measure your ground clearance you got now then subtract 1 1/2 or 2" from that to get an idea where they will be after the swap.