It depends how the pass is mounted. If the pass is mounted in a box with a slide over the front, with instructions to open the slide to use the pass and close the slide if you don't want to use the pass, then yes.

If the pass is glued to the window, then probably no.

(I'm speaking here in terms of passes in general, not Sun Pass specfically. and rental companies in general, not just Thrifty. I rent all over the country, in fact all over the world, with multiple rental companies, and notice in some places I get cars with the boxes with slides to open, and in other places I get a pass glued to the window. Since I never have my own pass, I haven't kept track of where I see which, I just remember seeing both. And since I usually keep my GPS -- which I always bring with me -- set to "avoid tolls", it's not an issue either way for me on most rentals.)

And thus how it's mounted may depend on the location where you're renting, as well as the rental company you're renting from.