I would sooner think a "split" personality would be the result of DS possessing MX rather than him literally having a split personality. Just look at Riku and the conscious struggle between him and Xehanort's Heartless. Others can see him as the normal Riku or the "evil" (possessed) one.
Plus, if MX is in the same state Sora was in, that would imply MX had to have already made a Nobody and fused with it, just like Sora, which clearly didn't happen.
Plus, if MX is in the same state Sora was in, that would imply MX had to have already made a Nobody and fused with it, just like Sora, which clearly didn't happen.