This would be a brilliant signing given the price tag, provided Van Gaal and the club doctors are satisfied by his medical reports. Sealing up the deal by pre-season would be ideal, then we can allow him some time to bed in, get him on a club regulated fitness regimen and assess the progress periodically. We have to consider that back injuries can be kind of debilitating for footballers who are used to consuming high calorie diets. Subtract the usual amount of training and match day rigors because of the back concerns, and it's no surprise that he ballooned up so quickly. Gundogan just has a naturally beefy figure and it's not necessarily a bad thing. These same issues cropped up with Shaw and Rooney, and it's kind of unwarranted. All that matters is performance on the field, not every player has to be shredded.
Anyway, if we had bring him along slowly and rebuild some of the drive and stamina he evidenced at his peak, then we could potentially have one of the Top 5 young-ish central midfielders at the club. He really has it all in his box. Combined with Herrera and Carrick, he would make United's midfield the best in the league. One thing to really like about Gundogan is his positional flexibility. He has played at #10 for Dortmund ahead of Sahin and Bender, in a midfield duo with Bender and in a pivot role with Sahin. He could be an upgrade in Fellaini's current position and bring some added creativity, or in Herrera's position freeing Ander to roam further up the pitch, or even in Carrick's current role (he'll have to brush up some of his positioning flaws, but Van Gaal can coach him up and he will have a good mentor in Carrick, who made a transition to that position). Also, his Sir Bobby-esque ambidexterous (ambipedal ?) style of play is very aesthetically pleasing and makes him a dangerous proposition in passing positions.