I'll see an errant line of pixels at an edge of the screen depending on what room I'm in (it's not very often), but never anywhere that bothers or disrupts my playing the game, and in any case, as NebulaBlue pointed out, you can just tell the 3DS to not stretch.
You say you're buying a new HeartGold, so if anything, I'd be more concerned about getting a possibly bootlegged copy. I would look into the game card, listing, who's selling it, or whatever if I were in your shoes, but in any case, an authentic HG/SS (or DS games in general) will play on the 3DS without trouble, and you can set scaling as you like.
^ The reason I say New is, I was looking through Amazon listings for new and although I realize they are way overpriced, that is where I had considered buying. But I plan on buying Used now due to said overpricing.