Yes - and no. As you said there are 39 points left to play for, but the reality is that 39 points isn't that many (as history as shown - there's normally not much movement in the table by this point in the season). For example - for United to make up 6 points by the end of the season playing at ... let's be generous here ... 2.12 points per game (the same as Leicester has to this point this season), they would get 27 points from those 39. That means City would need to get no more than 21 (1.6 points per game, or the pace that United and West Ham have played at to this point in the season).
So in short - if United suddenly plays like Leicester has to this point in the season and City plays like United have ... then United will possibly squeak 4th by 1 point. Otherwise, it's out of reach. The reality is that 13 games isn't that many, and clawing back 6 points (or .5 point per matchday) is very difficult to do. Yes, stuff like that has happened before. It's just not very likely to happen, that's all.
That goes for the title chase as well, by the way. Spurs or Arsenal have to claw back 5 points in 13 matches on Leicester, and Spurs don't get the benefit of playing them anymore either. It doesn't sound like much, but the reality is that being .5 point better per week is very, very difficult to do.