No i don't think US T4 is the counter to Wehr T3. With T4 you can hold off his T3 for sometimes but when he has 3 Stugs and starts vetting them up then AT guns is a must, with M18/Sherman fall back to support role (they are quite good at that).
As US, proper counter to T3 (or any Asix Armor forces late game) should consist of combine arms with AT gun as stoping power. You can't get away without it against good opponent.
I'd definitely second the need for AT guns against stugs. They beat both Shermans and M10s head on, and vet 2 makes them great vs inf. Personally i find tank depot at it's most useful after an extended t3 vs t3 battle, as ultimately Wher hold the trump card due to the nebel's ability to nobble your at guns.
P.S. In my experience, a fast tech to Tank depot should go hand in hand with a strong early game, which has left you feeling confident that tanks + AWM/Field repairs will win you the game.