Absolutely.
Many people who have problems with recoil use the 20 gauge for HD.
You'd probably what to use some type of standard sights, not a scope.
At the typical ranges of true home defense, the "bad guy" won't know the difference between a load of 20 gauge buckshot and a load of 12 gauge buckshot.
As I recall, there is actually little real difference between a 3" Magnum 20 gauge shell and a standard 2 3/4" 12 gauge, if you want to increase over and beyond standard shells in the 20.