Yes you would. You'd just have to make sure your bluetooth dongle for your computer is set up properly with all the proper drivers and what not. Then just sync your headset with your computer and you should be able to use it. Depending on the drivers that your bluetooth dongle uses though, it may be completely painless, or it may require some tinkering on your part. It also partially depends on your headset.
One thing you'd want to look out for if you're planning on playing online games with it is that you'd want to set up your sound to go to your speakers instead of the headset, unless you have a stereo headset (sound goes to both ears) then you'll want to make sure you purchase a bluetooth dongle that supports A2DP which will allow you to use your bluetooth headset with stereo sound.