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.
Thanks for the info. The i7 is a better chip than mine so it's probably not worth CPU mining I guess.