Of course! You just don’t get the cutscenes, or a couple of other perks, that come after marrying them. Or the minor hassles that come from them always being there.
You know whats beautiful about this game... You can do both. In 2 saves, in one save, in many saves on ALL the consoles or never. 10 years married to Abby (in 14 yr game) and I feel like at this point I have the best of both worlds. I play the game mostly like she's not there but she is and she's just too good to be true.
You can do whatever you want but if you don't marry you won't get all the stardrops, or children, or the random gifts they give when married, but stardew valley isn't a strict game you can play and enjoy it however you want.