TLDR; Yes a person would be reborn eventually if Balefired.
[Is balefire the eternal death of the soul?]
If someone is balefired, the Dark One can't reincarnate them. But they
CAN be spun back out into the Wheel as normal. Balefire is NOT the
eternal death of the soul. He also made a comment to the effect that
even in the absence of balefire, there may be circumstances where the
Dark One cannot bring someone back. There was a long line, so I didn't
The Wheel of Time Companion has this entry for Balefire.
balefire. An extreme weapon of channelers. It burned anything it touched into nonexistence and also burned threads from the Pattern, an effect which could destroy past realities. People who were balefired could not be brought back by the Dark One; however, their souls were not destroyed, and they could be spun out by the Wheel at a later time.
BRANDON SANDERSON (29 AUGUST 2011)
You have the right of it, Terez. I always believed that balefire =
Team Jordan instructed me that this was not the case, and balefire
meant the Dark One could not recover the soul.
From the Balefire Paradox
Ok, first and foremost we have an answer to the balefire-balefire
paradox. If A balefires B, then C balefires A, B WILL come back alive
again. I explored this quite thoroughly with him, getting him to
repeat himself more than once. It is definite. It is over. interview 16
This shows us that there is something to bring back, and the person is not permanently lost.
Balefire removes one from the Pattern, which is all the Dark One is able to influence. The souls themselves continue to exist beyond the Pattern, but how they are rewoven back in is less clear. It appears they spin back into the Pattern due to the Wheel itself, perhaps the Creator, or both.