"a closet" can mean different things to different people. If you are talking about raising and lowering a rack for something like AV equipment, there are ready-made solutions for that. But speaking of garage door opener specifically, I guess anything is possible but it won't be easy. It is a powerful motor connected to a very long screw that can transform the circular motion of the motor's rotor into linear motion of the nut traveling along the screw - basically what you need to move something up / down. I would imagine the device actually looks like a reversed scissor lift - the only way I can think of to conceal the screw itself (I am assuming "no tracks" also means no long metal screw along the wall either) so it is actually positioned up in the attic parallel to the ceiling.
Just curious what kind of a closet you are talking about and how much weight you are going to move and how far up/down.