Gotta have game time to do any kind of transfer.
To expand upon what Chops said... any "Character Service" requires all of the characters/accounts involved to have some gametime, and a
F2P with/after gametime is no longer a
F2P (it becomes Subbed/
VET).
So in
that sense,
"No", it isn't possible.
If you're not concerned with maintaing a character's
F2P status, then
"Sure", it's
technically possible... but with some caveats.
The only way I can think of is to lock-xp, buy a subscription, race change, then wait a month for your subscription to run out to turn xp back on and continue.
Is this true?
I don't know of anyone who's tried it during the
current patch, but the problem with your example (in the past) has been that characters that exhaust their gametime while "locked" get corrupted: they can't queue for
BGs, and they can't unlock their
XP.
Any "fix" or "workaround" requires
GM intervention... and has always involved eventually cashing-in the banked
XP, then getting "de-leveled". Saying that
GMs
"don't like to do that" is an understatement, but it
can be done.
If you're willing to risk it, my advice would be to contact
Blizz beforehand and say something along the lines of
"I want to give you my money for this service, but only if you guarantee to fix any resultant fuck-ups" (
but y'know, worded all "super-friendly n' diplomatic-like").
My only other notes would be that "getting gametime" doesn't
necessarily require buying a subscription... and "exhausting gametime" doesn't
necessarily require waiting an entire month (
GMs again).