I don't think Cuil has a chance of competing with Google; at least not for another couple of years. Personally I think the search results are not relevant and the way SERPs are displayed is not very user-friendly. Having said that, it won't hurt to submit your site to Cuil, so thanks for the post.
Cuil will have NO impact on Google. The results are no better, and I find the design annoying. It's too dark, the tree column results layout is bad. I am also seeing a lot of errors and "no search results" for a lot of terms. They should have done a lot more in private BETA before releasing it.