Doing both is definitely doable. 

You can't use cuda miner though on the CPU. You'll have to use something like pool's miner.  If you have a nice CPU there are some things to be cautious about.

1.  You'll be running CPU and GPU at 100% more than likely which if your PSU can't support will cause it to blow.
    - Games never use both at 100% so it will really stress the system
2.  You'll be outputting a lot more heat.  So things can get really toasty in a case.
3.  You won't get much more hash/sec with cpu mining.  As a benchmark I could only get around 90kh/s using an intel i7 4770k, and about the same with an i7 3930k
    - So you might be using more power than it's worth.