If the person is wearing a t-shirt, it might not work for a throw, but it would work just fine for a choke.
And if the person isn't wearing a shirt, then you wouldn't be able to use a shirt. That seems... pretty obvious. You'd probably want to also train for the contingency that the grips aren't going to be there.
Seriously. Aren't you the guy who went through a list of about 10 different scenarios where you're training with one arm, blindfolded, on uneven ground, etc? But the idea of training with grips and without is a serious conundrum? Come on, man.