Huh? What does "Nope" mean. This has nothing to do with a stud. We're talking about the bottom side of joists. It seems evident to me that the OP is talking about running the GEC in a way that creates a "clothes line". That would be a violation of 250.64(B).
No it can not be on the bottom of a joist. Nope for short.
Edit:
(D) Cables and Raceways Parallel to Framing Members
and Furring Strips. In both exposed and concealed
locations, where a cable- or raceway-type wiring method is
installed parallel to framing members,
such as joists,
rafters, or
studs, or is installed parallel to furring strips, the
cable or raceway shall be installed and supported so that the
nearest outside surface of the cable or raceway is not less
than 32 mm (11?4 in.) from the nearest edge of the framing
member or furring strips where nails or screws are likely to
penetrate. Where this distance cannot be maintained, the
cable or raceway shall be protected from penetration by
nails or screws by a steel plate, sleeve, or equivalent at least
1.6 mm (1?16 in.) thick.