In BF1 i shooted plane my video proof here - https://youtube.com/shorts/zyEjhHEYp24
But i had a Rifle yes not old Thompson

Even if it was a thing you could do in this game, you would not hit an aircraft with a submachine gun firing .45 calibre rounds.
Even if that was thing you could manage, you would need to hit it a lot to do anything to it.

TL; DR - submachineguns are low-power, short-ranged weapons

You'd need to borrow Jasper's M1919A6 to have a chance