Without going into all the details about no free breakers, location of
junction boxes, finished ceilings, etc., I'm looking for a "yes it's code"
or "no it's not code" answer to this question:

There's a junction box with a 14/2 without ground coming directly from the
panel. Leaving this box is a 14/2 without ground and a 14/2 with ground.
The ground wire is attached to the junction box but of course it isn't
actually grounded.

Can you run a single insulated ground wire from the panel to the junction
box to provide a ground for the 14/2 with ground that leaves the box.

The 14/2 without ground that leaves the junction box goes to GFCI
receptacle as the first receptacle on that run. That's fine for now.
However, the 14/2 with ground goes to some receptacles which should have
an
equipment ground. My friend would like to add that ground in the easiest
manner possible, which is to simply add a ground wire from the panel the
junction box. Can he do that?


*Yes. Check 250.130 and 250.120 for details. If he is able to pull a
ground wire, why not just pull a whole new cable?