I don't claim to know what was stated or heavily implied the last time the "scientific basis" of his revival from "decades of suspended animation" was discussed in any detail in a recent comic book story, but what you're saying is the version with which I've been most familiar for many years, and which I am perfectly willing to accept as the basic excuse. In other words: the Super-Soldier Serum acted as a sort of "antifreeze" which prevented drops of water in his brain (and elsewhere) from turning into nasty little ice crystals which could rupture the surrounding cells and cause permanent damage. But the reason he didn't look any older when he was defrosted in "Avengers #4" was simply that his chilled body hadn't been doing much of anything in all those years when he was "on ice."
Likewise, that's the version that makes more sense to me -- even if the Serum "keeps Steve young," withdrawing the serum should simply mean "he's now a perfectly normal human being, with the same height and build and youthful skin and muscles and very healthy internal organs and so forth that he had yesterday morning -- except now he's going to start aging normally from this day forward, same as anybody else -- unless and until he gets the serum back!"