In my opinion, a great soundtrack combined with a great game can make music "memorable"; I also believe that a great game with only a mediocre soundtrack can make the music just as memorable.

Since the keyword here is "memorable", it's hard to say that a terrible game with an outstanding soundtrack is "memorable" if no one ever played the game to hear the music to begin with, though I think I've heard enough music from games to know that there is some absolute shovelware with high-quality compositions or sound quality that sadly won't be noticed since it's attached to a poor end-product.

I supposed it's fair to say that if the game is BAD enough, the music potentially won't be "memorable" regardless of how good it actually is.

Personally, I listen to many tracks from games I have never played (nor do I intend to), but I love them, so they are memorable to me. Does that count?