They can play him. They'd have to drop Ibrahimovic or Iniesta though. And the highly promising Pedro (who I'd put at at least Ozil's level) would remain a sub. Not impossible, but they'd really be spoilt for choice. If Fabregas then went, it would be fairly crazy.
Mind you, and without suggesting that we have the same quality in midfield, it's not THAT dissimilar for us. It would be fairly easy for him to play in the hole in the tough matches where we go 4-5-1. In other games, we'd have to drop Berbatov, which would I think be a shame as it would kill his chances of doing himself justice, or one of Valencia or Nani, who don't deserve it and who are at the same level I would say. While he's clearly a very promising player, and very tempting, I don't think he's a no-brainer for us. We could actually do with more of a physical attacking player for midfield/attack I think.