Hi,
I don't think there is a simple, F5-supported way to give unauthenticated access to just the pool stats page. However, you could create a guest login and use that. In the upcoming v11, you have the option of not enforcing the GUI's idle timeout on the dashboard using a checkbox under system>>preferences:
Enforce Idle Timeout While Viewing The Dashboard
If that doesn't work for you, you could modify one of these examples:
iControl-based solutions which allow programmatic access to the BIG-IP
http://devcentral.f5.com/wiki/default.aspx/iControl/codeshare - search for "status"
http://devcentral.f5.com/wiki/default.aspx/iControl/BigipBlogging.html
iRule based solutions which use an LTM virtual server to get the status:
http://devcentral.f5.com/wiki/default.aspx/iRules/codeshare - search for "status"
http://devcentral.f5.com/wiki/default.aspx/iRules/Pool_Member_Status_Page_on_a_Virtual_Server.html
http://devcentral.f5.com/wiki/default.aspx/iRules/Current_Pool_Member_status.html
Aaron