Understand how Cloudflare integrates with Google Analytics.
Overview
Since Cloudflare does not proxy Google traffic, Cloudflare has no effect on Google Analytics (GA) tracking. Your site visitors will interact with Google's servers directly. The Google Analytics Javascript code on your pages is executed by the user's browser, so Google Analytics sees the IP of the user's browser. The GA Javascript code on your page doesn't talk to your site, so it doesn't interact with Cloudflare.
Cloudflare proxies traffic to your origin web server. Therefore, the Cloudflare connecting IP matters only for any programs that read logs directly from your web server (like awstats).