I've had random thoughts about it before, just because I like rear suspensions, but usually think more brat-style bikes look a bit cluttered and uneven. The only way it'd realistically be possible, is if you were to fit some type of hinge to the bottom portion of your frame at the chainstays, up closer to your battery. Then you would need to cut out a portion between the axle and rear seat to fit the rear shocks. I feel like if you can weld and have the steel and some bushings, there's no reason it couldn't be done. You'd basically just be turning the bottom portion of your frame into the swingarm.
I've seen mountain bikes with similar arrangements. They appear to be hardtails, but there's a smaller rubber bushing right behind the seat post, and usually the bottom of those frames just flex, and don't actually pivot, but it's the same idea. I can't find a good picture because I don't remember what bikes they were, but this picture was the closest I found in my 10 second google image search.
Now the one remaining thing you'd have to sort out, is if you were to fit a pivot point at the bottom of your frame, the rear axle wouldn't be moving perpendicular to the chainline, which means your chain would get tighter and looser every time the suspension compressed. That would also mean that every time you gave the bike some gas or let off the gas, it would compress or expand the rear suspension somewhat, affecting the handling of your bike. Overall, I think that part alone would be enough to make the whole project a bad idea.
