"Is there any benefit to installing a GFCI outlet to an older circuit that has no ground wire?"
A GFCI (ground-fault circuit interrupter) reduces the risk of electrocution by constantly measuring & comparing the current coming in on the hot wire with the current going out on the neutral. Any difference in the current means that electricity is flowing back to the source on some path other than the neutral wire. That other path may be through your body to the ground, & that is what a GFCI is designed to prevent.
A GFCI works as well without an equipment grounding conductor (ground) as far as preventing electrocution, But beware of using computers or other electronics on this ungrounded circuit, however. GFCI will protect people from shock, but will not protect equipment from lightning/ spike damage even with a surge protector & electronics also use the ground to dissipate static charge.
Any outlets downstream of an ungrounded GFCI outlets that have ground slots should also be labeled "no equipment ground".