Well, I dont actually know, cause I havent tested it. But tbh I cant see that happening, so far relationships only went up/down when I was actively playing that household, I dont think the game does anything with inactive households (not counting neighborhood stories), especially when it comes to relationships.
Also from what I learned it's the romantic satisfaction meter that you have to "work on", if it is high enough their romance bar will increase over time on its own but Im guessing (again) this will only happen when the household is actively played.
Right now one of my couples has a high romance satisfaction, Im about to play a different household for the reaper thingy and then come back to them, can report if anything changed later.