Midnight Lulaby

I think so, because before Twilight's transformation, she wasn't a princess, but after season 3, she is. So it seems that the instant you become an alicorn, you're a princess. But I could imagine there being an evil alicorn who wasn't royalty, because, you know, they're evil. (Nightmare moon was royalty, she said so herself, and she is technically princess Luna, and chrysalis, hope I spelled that right, was a changeling, not an alicorn.) So I could imagine there being an alicorn who refused the title of princess, or prince (alicorns can be male, right?) and sort of just...Did their thing, evil or not. But if Celestia would allow an alicorn simply to refuse the crown, I'm not sure, Twilight didn't want to be a princess, but she did anyway, but I think she did that for the good of equestria, rather than because she had to. So, my answer is... Being an alicorn gives you an entitlement to royalty, but if you don't want to be a princess/prince you can refuse.