No; Manchester United football ground is adjacent to the Manchester-Liverpool via Warrington Central line (CLC, Cheshire Lines Committee) but not close to your route. If you're going over the Ordsall Chord (so Manchester Piccadilly to Oxford Road to Deansgate to Victoria) you will probably be able to see the ground on the left-hand side of the train though.
If your train reverses in Manchester Piccadilly then you'll definitely see the Manchester City ground but that's not what you're asking.
Essentially, Old Trafford football ground is to the west of the city centre and if your train uses the Ordsall Chord then it loops to the west also; otherwise it doesn't. City's ground is to the east of the centre (it used to be south, but that's been turned into houses!).
(1) below shows where Manchester United is; the Ordsall Chord isn't shown but it runs from Deansgate to Deal Street Junction. Your route from Manchester Airport brings you in through East Didsbury.
