We go to old Trafford on September 17th. If we were to have Costa in doing a medical tomorrow (Aug 29th) and he sailed through it, he'd have 18 days to get match fit. Considering he hasn't done anything since stomping off in a huff from Chelski, there is zero chance of him getting match fit in 18 days. Absolutely zero. And his agent would advise him not to try, because any injury would cause him hassle with Atleti.
If we got him in on Aug 30th, following the hypothetical medical on the 29th, the earliest we could realistically expect him to be match-ready would be thirty days, and that would be pushing it. That means he'd be touch-and-go for October 1st against Burnley at Goodison - exactly the type of game where he'd get lumps kicked off him and probably retaliate. Straight red means a three match ban, so that's Brighton away, Arsenal at home and Leicester away he misses. He would come back for the 5th November game against Watford, but be eligible for the Lyon games before that.
Realistically, you're talking about having him for November and December, and HOPING he actually puts a shift in prior to leaving on January 1st.