No, that isn't correct. "Just because" in that sentence is used in the sense of "since"; in trying to understand the sense in which it's being used, it should be acceptable to discard "just". It would be closer to correct to say something such as, "Because I stopped eating, I must be full", even though clunkily back-to-front, but one should not use this sort of construction to convey the opposite. The speaker/writer is simply choosing the wrong construction to mean something like "The fact that I've stopped eating should not be taken to show/mean/imply that I'm full." "Just because" means "only because" in that construction, and it's incorrect to use a conjunction there in that way. Also, on a logical basis, of course it can't be literally true that any person who has stopped eating can be assumed to be full.
(ETA: Note that describing something as an "decoding idiom" or suchlike terms, as in a linked paper from another answer, does not support an argument that the construction fits existing grammar rules. There's not much room for argument that this is proper grammar, though it may be so common that we should accept it on that basis.)
I don't think that's the end of the inquiry, though. This sort of construction is used all the time by real people, and might form part of believable dialogue for many types of characters: a child, adult without much language-arts education in English, a smart person proud of working-class roots, etc. You know the people I mean — the same ones who might say "I could care less" without agonizing over whether they're being sarcastic. If it feels right, it might be right in context. Real people can be expected to use incorrect grammar in a wide range of situations, and acknowledging that might sometimes be to the aid of realism and character development. I'm reminded of Michelle Pfeiffer's Frankie yelling over a bathroom stall at Al Pacino as Johnny, "Fuck you, how I talk!"