Yes you could use it to mine. Just SSH into it (I assume it's running Linux) and set up like normal from there.
this only works if your server has a graphics card. if you're going to mine with the CPU, don't bother, because it generates very little bitcoins.
Well, I figure I could run it in conjunction with my efforts at home. It's free CPU bandwidth I'd still be paying for anyway. Costs me nothing extra to run it