I agree with, like, half of everyone here. It would have to be more than the romance, but yeah, it's feasible. You'd just have to make it closer to just your bog-standard slice-of-life school roleplay, but with the twist which is usually taken up by something like "Blah blah magic" being that life works like a harem anime. Personally, I'd thrown in some mention of current events (Maybe it takes place twenty minutes into the future, or maybe the Cold War is still going on like in Full Metal Panic, maybe the whole school is actually on a generational starship or some other crazy thing like that), then let people get mixed up in the results of those events/have them be a part of their backstory. It could be a fun way to play with anime tropes (The mysterious shy girl's parents were killed by the Soviets and she has PTSD! The uppity, rich tsundere is the Captain's daughter!)
But, in the end, a roleplay based entirely off of the usual harem antics wouldn't work out. It really has to have some overall plot (They're learning to something something warfare/the evil empire's gotta go down), or be really, really character driven.