Fab Melo does not have what it takes to make it as a Celtic, from a mental/cultural standpoint, considering what his teammates would be asking of him... in my opinion. From my time at SU with him, and from my time as an intern with SU Athletics, I can tell you that he in no way, shape or form has the characteristics that qualify as being a Celtic.
Don't get me wrong, he's a really nice guy and good person, and he's a talented player when he puts his mind to it. However, he just doesn't care about the game of basketball very much at all, and that would make for a terrible mix in culture with the way the Celtics are currently constituted.
I think he could end up having a few semi-productive years in the NBA, but he just doesn't have that winning mentality or love for the game that I believe the Celtics look for in their players.
So, to answer your question, while I believe that Fab possesses certain attributes that the Celtics could use (size, rim protecting ability), he is still a very raw talent with very questionable mental toughness, and I would be disappointed if the Celtics drafted him.