I agree it could be possible. I don't really believe or not believe it so much as I'm pretty much open to all the possible ways he could be connected to her (student, related, follower of her legend after she'd already been imprisoned, etc.). A few others seem to think that too.
I don't think he's fighting for the throne though, but only because his plans just get increasingly convoluted that I have no idea what he wants, and at this point it could be something as extensive as totally subjugating Mewni or whatever.
His regeneration could be a result of some weird combination of natural Septarian regeneration mixed with natural Mewman magic. Although the problem here is that Eclipsa's monster lover clearly doesn't look like Toffee.
I think it's still possible he could've been adopted or something too though. since we don't even know if it'd be possible for Eclipsa to have children with a monster-- which would account for his different appearance. In that case (or if he was her apprentice/student) his immortality could be a result of a spell or something from her.
More than anything I'm starting to get the impression that Heinous was Eclipsa's descendant though. Eclipsa could've had a child from her first husband born after she'd already left (I guess an ancestor of Heinous? she's probably not that old). Heinous isn't known to be part of the Butterfly family, yet has the cheek emblems and a thing for monsters, enough that St. O's has features resembling a monster temple.
We know Toffee and Rasticore are connected at least, in Moon's tapestry and going by them both being "of Septarsis," and Heinous seemed to have a thing for Rasticore in his last appearance.