C172s,
No, you won't be able to do rnav approaches. Read this link:
http://www.ecacnav.com/rnav/default.htm
in the sequence presented and all will be revealed. my guess is the navigation system presently on board will meet rnp5. however, rnp1 will soon be required for terminal area nav and that is the standard most likely to get you to the final fix. beyond that, rnp0.3 will be required for final approach. most boxes without gps will never get the tick and with the world wide trend to disabling the ground based aids in favour of spaced based systems, no valid updates will be available to get ins/irs even close.