Probably. According to the index to the Unfinished Tales, 'Easterling' is (in Third Age usage)
a general term for the waves of Men driving in upon Gondor from the
eastern regions of Middle-earth
The grouping includes the Wainriders and the Balchoth but not the Variags of Khand, who are listed separately among the combatants at the Pelennor Fields. If we accept the main version of the Hunt for the Ring as canon (a bit dubious since it does not appear to have progressed beyond a fairly rough state) then either:
Khamul is an Easterling. This agrees with the rejected version and fits with his description as the 'Shadow of the East' in the main version.
Khamul is not an Easterling, but travelled to the east (perhaps sent by Sauron)
and there gained the epithet 'Shadow of the East'. This agrees with the main version but not the rejected version.
I would be minded to go with (1), but I don't think there is any absolute proof.