Mendicant's core is still in Zeta Halo. But the AI itself is in the Ark. If anything, some crazy plot twist could happen and then he could appear. But I think it's better if that didn't happen.
I don't think one can say that MB's "AI"--maybe by that you meant his matrix, or his source code, or something like that--is still on the Ark. The Halo 3 final Legendary terminal makes suggestions that MB died (or at the very least expected to die). A few excerpts of importance:
Quote:You don't know the contortions I had to go through to follow you here, Reclaimer.
I've always understood this message to mean that MB transferred himself onto Installation 04b itself, after the part of him that hitched a ride on the Keyship recombined with the part that was imprisoned on the Ark.
Quote:I know what you're here for.
This is MB saying that he knows Chief wants to fire the premature ring.
Quote:And so here at the end of my life, I do once again betray a former master. The path ahead is fraught with peril. But I will do all I can to keep it stable - keep you safe.
This statement suggests that, knowing the ring would not survive a premature firing, it would result in his destruction as well. But he was willing to make that sacrifice in order to keep it together long enough for the Chief to escape after firing it; I don't think it was just luck that the ring self-destructed in a way that happened to leave a clear path for Chief to use to get back to the Dawn
. Also MB could have been the one that kept the control room doors locked closed to keep the Flood out. Perhaps Bungie's thinking was that MB needed to be on the ring itself in order to interface with it's systems effectively; remote access from the Ark may not have been an option.
I always found this train of thought to be quite compelling: MB sacrificing himself to help Chief stop the Flood. A noble gesture that would be lessened if he'd somehow survived. Of course, with MB being an AI, we can't really confirm death like we can with other characters. We can only infer from what we're given in the terminals, which represent the last known instance of his actual presence. But I think my interpretation of his final terminal message is very fitting.