There was another thread that touched on a similar topic–whether or not ROs should hook up with other characters. But that was “if they aren’t romanced,” not “should you have to fight for them.”
I really agree with @Mewsly that it could be easy to make it feel like the MC is getting between the RO and their actual true love, which would make me pretty disinclined to pursue them. But it might also feel like the MC is the second choice, or lesser option, or that the RO isn’t as into the MC as the MC is into them. There’s some old adage (that I couldn’t find a quick source for), “I will fight for you, but I won’t compete for you,” that’s pretty relevant. I don’t mind an RO who’s a bit of a challenge to romance, but I don’t think I’d enjoy it much if they were just constantly flip-flopping between liking my character or liking some other NPC better.
It would probably work more if there were some conceit in play to make it less about who the RO’s crush is bigger on–like, RO has a suitor who’s a better financial, political, social, what-have-you match as opposed to the MC, who they will agree to be with if the MC is a better personal/romantic match, something like that