Personally I don't think that they will start winning all their games magically after Ozil get in the boat but certainly they will play better than this in EPL. Actually in some teams I believe that the coach is not doing enough to stimulate the players.
Imo, it's the duty of the player to work hard and give the manager a reason to play him, I'm sure if Mesut Ozil was playing and Arsenal are having this bad run, fans will still find some other excuse to make and criticize the manager, Arsenal are in a bad run and Ozil is not going to change anything even if he gets on the pitch, the last games I watched Ozil play in an Arsenal jersey, I must say he wasn't impressive and if the manager decides to drop him, it's cause he doesn't think he has anything more to offer the team, the coach wouldn't stupidly bench a player that would change his teams fortune.
4 consecutive wins in the EPL for Man United I think it's been a tough week for the two Manchester who will face this week although Gunnar Solskjaer will be full of pressure if he loses maybe he will be sacked soon if it loses.
For sure there'll be a lot of pressure on OGS If he loses to pep tomorrow, but I don't think he'll be sacked by the United board if he loses this game, I believe United will give him the chance to finish this season before assessing the teams performances, plus trophies, before taking a decision, many times changing a manager mid-season doesn't change anything, though it gives the new gaffer the chance to get to know his players before the start of the other season.