Can I splice a ground wire from old wiring to a GFCI outlet?
GFCI's don't actually require a ground wire, so it is legal to continue as-is. 

Attaching the ground wire is worse than useless unless the ground wire you're attaching is actually connected to the house's grounding system.  So that's worth checking.  I would look for zero-ohm resistance between the ground wire and nearby water pipes, if they are metal.