Not really, he will be the second choice for the right centre back position after Pique.
The other three are all left CBs or LB/DM.
He could even get minutes at RB before xmas if Montoya and Douglas go.
Mascherano is often played on either side, depending on who his partner is. Him playing DM is such a rarity that it shouldn't even be counted as a factor. Kind of like when people mention Douglas when discussing the RB position.
Ignoring the fact that Pique is by far our most important defender and is unlikely to miss more than a small handful of games, Mascherano can play that position as well and if Pique were to be injured I can guarantee you we'd see Masch playing next to Mathieu or Vermaelen.
On the left CB position, that is a position Bartra played quite often as well, which is part of why his minutes took such a large hit from last season. When Pique needed a partner because Masche was injured/subbed/rested that guy went from being Bartra to being Mathieu. When Mathieu was injured Bartra got those minutes, but now Vermaelen will be there, hungry for minutes of his own.
I wouldn't expect to see Bartra play at RB, either, even if Montoya and Douglas leave. Lucho doesn't seem to be a fan of the idea at all and Alves kind of has the position so tightly locked down that I'd be worried for my own playing time if I were Vidal.