Yep. This is what I do. I have a couple of large plastic Tervis glasses that work great for this, and as a bonus if I've put too little ice in or heated the water too much I can adjust on the fly by seeing through it.

Even better: I aeropress onto a cocktail shaker with ice, then shake the hell out of it. The coffee get's very cold much faster, and I just throw out the ice and sometimes put nice new cubes in at the end. The coffee comes out a bit frothy and tastes better than any variation I've bought.