No.
This vehicle is outside of the 10 year limit on the duration
parts need to be held for safety reasons. Not only will they not
fix it, you may not be able to get the parts period.
The only reason they may fix it for you is in case of a
recall.
Check out
http://www.recalls.gov/nhtsa.html
Recalls specific to 1991 Honda Accord.
http://nhthqnwws112.odi.nhtsa.dot.gov/acms/docservlet/Artemis/Public/Recalls/1993/V/RC-93V056-NN.PDF
http://nhthqnwws112.odi.nhtsa.dot.gov/acms/docservlet/Artemis/Public/Recalls/1995/V/RC-95V103-NN.PDF
Here again, your vehicle needs to fall within a certain set of
guidelines to even be considered for the recall fix and ONLY your
dealer or customer assistance center (see owners manual for phone
number) can tell you this, anyone else is a matter of opinion.