It depends on how busy this affiliate system is going to get. And what approval system you had in mind? I mean - for you is the approval system just a rubber stamp? If so, just go ahead and do automatic approval. It will save you time in the long run. And some people might not want to sign up knowing they might have to wait. (we are in the internet age where everyone expects it yesterday.)
I know that we run two different types of affiliate system on our websites. One, is just a basic link / banner link to our website. These people are approved right away. No waiting, etc. The other one, well they are still approved right away, they just have to sign an application.