If the OBDII system has not been reset recently and the battery has
not been disconnected then I would suspect you are ok. An exception
seems to be model year 96 where (from TSB 2334):

When interrogated using a generic OBD II scan tool, the MY 1996 Volvo 850, equipped with Bosch Motronic 4.3 Engine Management System, may experience all of the Readiness Codes changing from COMPLETE to INCOMPLETE when the ignition key is cycled.

Ouch.

Volvo has TSBs with the reset procedure and customer interview questions
to ask after an OBDII test rejecttion -- there are several TSBs at
www.alldatadiy.com. They do seem to indicate this issue applies to
96, 97 and 98 model years.

I note the TSBs say help the dealer provides is a warranty item under
the 8 year/80K emission warranty. Don't forget, emissions have longer
warranty then the base warranty. Some states may require longer warranties.