While, technically, running an EGC separately from its circuit is allowed by code as per 250.130, paragraph 2:
For replacement of non-grounding-type receptacles with grounding-type
receptacles and for branch-circuit extensions only in existing installations
that do not have an equipment grounding conductor in the branch circuit,
connections shall be permitted as indicated in 250.130(C).
(C) Nongrounding Receptacle Replacement or Branch Circuit Extensions.
The equipment grounding conductor of a grounding-type receptacle or a branch-
circuit extension shall be permitted to be connected to any of the following:
(1) Any accessible point on the grounding electrode system as described in
(2) Any accessible point on the grounding electrode conductor
(3) The equipment grounding terminal bar within the enclosure where the branch
circuit for the receptacle or branch circuit originates
(4) An equipment grounding conductor that is part of another branch circuit
that originates from the enclosure where the branch circuit for the receptacle
or branch circuit originates
(5) For grounded systems, the grounded service conductor within the service
(6) For ungrounded systems, the grounding terminal bar within the service
(2) Grounding and Bonding Conductors. Equipment grounding conductors shall
be permitted to be installed outside a raceway or cable assembly where in
accordance with the provisions of 250.130(C) for certain existing
installations or in accordance with 250.134(B), Exception No.2, for DC
circuits. Equipment bonding conductors shall be permitted to be installed on
the outside of raceways in accordance with 250.102(E).
I would prefer a retrofit using a GFCI or DFCI circuit breaker or GFCI receptacle as allowed for in 406.4(D)(2):
(2) Non-Grounding-Type Receptacles. Where attachment to an equipment
grounding conductor does not exist in the receptacle enclosure, the
installation shall comply with (D)(2)(a), (D)(2)(b), or (D)(2)(c).
(a) A non-grounding-type receptacle(s) shall be permitted to be replaced with
another non-grounding-type receptacle(s).
(b) A non-grounding-type receptacle(s) shall be permitted to be replaced with
a ground-fault circuit interrupter-type of receptacle(s). These receptacles
shall be marked "No Equipment Ground." An equipment grounding conductor shall
not be connected from the ground-fault circuit-interrupter-type receptacle to
any outlet supplied from the ground-fault circuit-interrupter receptacle.
(c) A non-grounding-type receptacle(s) shall be permitted to be replaced with
a grounding-type receptacle(s) where supplied through a ground-fault circuit
interrupter. Grounding-type receptacles supplied through the ground-fault
circuit interrupter shall be marked "GFCI Protected" and "No Equipment
Ground." An equipment grounding conductor shall not be connected between the
because such a retrofit is much less labor-intensive for the electrician, will be safer (as someone may unknowingly unhook a separately routed EGC and fail to reconnect it, whereas a GFCI's protection is always there), and doesn't create a massive current loop in case of a low-level ground fault, with its resulting magnetic EMI and possible magnetic pickup of stray voltages and RF.