Yes, and at the moment it's free. I read some posts that they made the service free for a limited time in 2015. Seems to be a quite long limited time. I love it!!!
I'm not sure if it would be possible to make TG accept these FBX objects. Mixamo builds some bone structures, skins the mesh and applies an animation to it, if you like. Even with an ultra long animation the file size stays more or less the same. Endless possibilities...