Stats virtual directory creates under application pool " DefaultAppPool " and it will connect using Application Pool Identity. We have tested and confirm locally that it is not creating any problem.
Secondly, it would be better that HC creates all virtual directories with same pool under which a website is running (dedicated pool). This will be implemented in any of upcoming modified build installer.
Also I would like to mention that with click apps we recommend PHP version 5.2 it is listed in this
Article. FasstCGI is not currently support in the HC Panel as well as PHP ver 5.3 is not yet been tested & approved with click apps list.