Cloudflare should not impact Ajax functions on your site at all. If you do see an issue with Ajax on your site that appears to be related to Cloudflare, please open a support ticket and we'll take a look.

Note: You should confirm whether the issue is caused by Cloudflare or not at all first. If you pause Cloudflare in your settings, then you should be able to see if the behavior still happens with Cloudflare off.