Would he still be able to function as a Superhero after being exposed to Gold-K and losing his powers?
Your post title says "hero", then you say "superhero" and mostly talk about how his powers work.
I don't think anyone here doubts he'd be a hero.
As a superhero, though... I dunno. Is Batman a superhero? Is Luthor a supervillain?
Really, this gets back to where Superman's powers come from. Is it gravity, solar radiation, atmosphere conditions (an explanation for his powers that was eventually dropped), a mix, etc.? How do his powers work?
Does he have "powers" that are purely a function of his physiology? Should Kryptonians be better able to retain extract oxygen (or perhaps alternate power sources) from whatever is in their lungs (including water) to account for Krypton's noxious atmosphere? Should Kryptonians be able to see in the UV and IR spectra and avoid easy blindness because Krypton's lightning extremes are so intense? How smart is the average Kryptonian and why? Are there extra organs on Kryptonians?
I think the only way that Gold K makes sense in its portrayal is if it literally turns him "human" (not just removes his powers), or if there's only one power source for Superman's powers for it to short-circuit. Canon on the latter has varied over time.
I'd like the idea of Superman being "1938" powerful even if the energizing effects of particular frequencies of solar radiation were taken out of the picture. It'd be nice to see more of the "leap tall buildings" aspect.
Would he still function as a superhero? The most recent incarnation has Superman more or less not wanting his powers, his powers going away for a year (with all sorts of "powers" implications), and him being a crusading reporter. Earth-2 Clark Kent did much the same thing after The Wizard "buried" Superman.