No, not at all. If you use Google Analytics or a system that tracks logs through a script on your web pages, then Cloudflare does not affect any of your Google Analytic tracking. We have actually built a Google Analytics app so you can make sure that Google Analytics is installed on all of your pages.
It is important to only have one instance of the Google Analytics tracking code on your site. Having multiple instances, which can occur by manually adding the code snippet and enabling the Google Analytics App for the domain, will likely result in double the amount of statistics reported by Google as both instances of the snippet utilize the same six tracking cookies.