Unfortunately, I don't see him getting many ABs initially. The O's have a ton of OF and seem committed to using platoons in LF (Rickard/Kim) and RF (Smith/Gentry), Trumbo as full-time DH, and Crash at 1B.
If Mancini can get himself involved in the RF platoon, that's awesome, but he's never played a regular season game in RF, and only a handful of ST starts (LINK). Buck has shown that he's willing to let players who hit man RF (e.g. Trumbo in previous years), but they're trying to get some better OF defense this year.
However, with their histories, there's a decent possibility that Smith and/or Gentry will get injured or released due to poor play. If Mancini keeps hitting and shows he can play the field, that'll help with the latter.