Might work... afterall how many times has the Red Skull come back in new bodies, same mind and soul, different body. So it might work. Although I keep thinking that his own body could regenerate somehow... (I never read that issue where his body kind of shrivels up) but maybe that's what the SSS needed to do to repair the damage from the gunshot wounds. Essentially it took all the strength from the rest of the body to repair the damage, but when the damage is repaired maybe it'll take a little while for the body to rebulk itself back up.
What could be interesting for a while... have Steve return basically as a fit yet normal guy. Not a skrawny 98lb weakling, but an average build and strength. And see him gradually rebuild himself on his own. He's still got his keen tactical mind, he's still got his spirit, he just can't jump across buildings and kick as much ass as he once could. He's still Steve Rogers. He's still a strong leader. He's still an icon. But he wouldn't be "super" for a while... which means he doesn't have to register as a superhuman, nor would he be treated as such. Not to say he's a pushover, he just has to use his brain and other skills more than his physical ability, which HAS been what Cap was always about.