yes.
it would depend on the specs of the computer. if it is only a dual core, you could mine with only 1 thread and it will use up 1 core, but depending on the processor even 1 less core could even bog it down a bit. it really doesn't hurt to download a miner and try it. find out for yourself.
If you are mining in a pool, and are really lucky to get a lot of blocks through the month, perhaps? but in my experience you might break even or even not. lets say you're mining both cpu and gpu and you're using 200watts for 30 days straight and your electric costs 12 cents/kilowatt. that's a little more than $17/month right there.
As i mentioned a bit earlier, all I can advise is to find a nice pool to join and mine with them to increase your chances on finding a block and getting paid. And a little tidbit, if you join a smaller pool, you might not find blocks as often, but it will help make the network more diverse as well as possibly increase your chance at getting paid more.