At the sub shop where I work, that is how we serve a gyro-on a low carb wrap.(Tortilla)It is tastier that way instead of on our bread(which we bake 2x per day)because the bread overwhelms the meat, etc…

you can put just about any meat in a tortilla wrap.
A gyro wrap might be a good idea too, especially if you want a gyro when travelling, without the mess.

Sounds pretty good to me. I would just be sure the tortilla is fresh and maybe heated up a bit. You may have to double it over to guard against tragic rips.