You are correct. I just tested Zelda:DX on my hardware SGB, and it does indeed include a border (although that seems to be the only SGB enhancement, unless there are sound samples somewhere in the game).
Also, I would differ with you on the SGB statement - since no other system supports SGB enhancements, I would consider SGB games to be their own format (with the knowledge that the work on a regular Game Boy with reduced functionality). Especially considering that there was at least one game (Space Invaders) that included a version of the game in native 65186 code that could use the full SNES graphics and sound capability, which means that these games only run to their fullest on a SNES+SGB.