I mean, I guess it depends on what you consider "reincarnation" to mean. In the context of Metal Gear, you have three basic methods of reincarnation:
1) Literally cloning someone (Solid, Liquid, and Solidus Snake)
2) Body doubles/psychosis (V and... maybe Liquid Ocelot?)
3) Training/Mentoring(All of the Snakes except Venom, Ocelot, Raiden)
Strangely enough, the only one that even seems to remotely work is 2, considering that both occasions were largely successful. Cloning Naked Snake/Big Boss produced three Snakes that all ultimately rebelled, in different ways, against their creators. While it's tough to say what Naked Snake/Big Boss' goals were in mentoring Ocelot, he seemed to be the only person Ocelot never actively betrayed. However, the Boss' mentoring of Big Boss, Big Boss' mentoring of Solid and Liquid Snake, and Solidus Snake's mentoring of Raiden all failed in one way or another.
On the other hand, V ended up both becoming Big Boss and remaining loyal to the cause after finding out. Liquid Ocelot successfully hypnotized himself and followed through in his goals. (Granted, the latter case is arguable. I always liked the idea that Ocelot was acting the entire time.)
So anyway, the point I'm kind of getting at is that, if your theory is correct, Sunny sort of exists as a fourth sort of reincarnation in the MG universe, since neither her parents nor anyone who mentored her ever met the Boss. (I think? I don't recall her father off the top of my head.) But she still seems to be carrying on the message of the Boss into the epilogue of the series. Granted, I'd say it's likely more of a thematic thing than an actual character trait, since one of the big overarching themes of MGS4 is that of cycles.
Of course, this is all postulation and theorizing on my end anyway.