Hardly doubt it. His frame, and body will struggle in the epl to deliver same levels for at least a year, which is my guess. Cafe likes to big up this signing like those you mentioned but here the game is way more different than in Bundesliga and specially Dortmund. Every Dortmund players struggles in different teams which is a history you can not deny, from Sahin, to Kagawa, gotze, mkh, dembele didn't hit the ground running as well, though he was more developed than Sancho both game wise and physically, but Barcelona had the players to take pressure off him with their elite stars.
Surely he may be a very good player in the future, even in epl but at the moment he is not ready to take the league by storm for the fee which is quoted and that along with media and united fan base adds a whole lot different pressure he may struggle to cope with it with the demands of tough competition in the league both intensity and physical wise and may be he will lose out his place to lingard again when he struggles for form or with tiredness. I thinking waiting a year makes much much more sense and if he develops the same rate of even further the fee to get him next year won't make much of a difference to be honest and he will be better tested and more experienced and developed for the challenge at united.
I think we should use this money a whole lot better this season than splashing very big cash on a still developing 19 year old and get 2 other options for that price including a midfielder and another wide player capable of playing on the right and or may be on a loan.
Its good to plan and get players as a long term investment plan though it must be backed with the short term success to smooth the initial transition period and I feel this transition period he will be better equipped to handle if he plays another season at Dortmund and shine.