I could see this working just fine, yes.
The other possibility is that the "mother culture" from which the Ba'ku colonists came, the "solar system on the verge of self-annihilation", is in fact the Son'a home system and is still populated by millions or billions of members of the species.
A group of Son'a left, found longevity, and started calling themselves Ba'ku - and then some of them
left, stopped calling themselves Ba'ku and returned home. Reporting on the discovery of longevity, they managed to get the mother culture to rise up in arms against the colonists. The culture gave them the battleships and their crews - but the individuals commanding those battleships were the especially bitter ones who had been exiled by the colonists.