Some of the heat given off by that light will come from the ballast, yes. So relocating the ballast away from the bulb will drop the temps slightly, but in my experience even a 600w ballast in or out of a room will only make a few degrees of difference.
HPS will run hot, the only thing you can really do is cool the bulb. Not by blowing air at it, that would just spread the heat around the room. The best thing is to vent hot air away from the bulb and out of the room. If you remove the ballast it will make it easier to cool, but it won't make it a great deal cooler on it's own.