Probably not. Could turn up on a railtour. It would be dependant on signalling systems and the crews route/traction knowledge.
There won't be connecting wires from the WCML to GWML for a long time (CP6).
Wiring of the short but awkward gap from Acton Wells (NLL) to Acton GW (over the "Poplar Branch") has been postponed.
But nothing to stop an 86/87/90/91/92 running Paddington-Bristol (Parkway before Temple Meads) or Cardiff when wired.
Or a 313 or other ancient EMU.
I don't think anybody has proposed electric freight on the GWML yet.