1. If a Western Dwarf were to turn to Chaos, would it be possible for them to join the Chaos Dwarfs?
2. Would the Chaos Dwarfs accept this newcomer?
3. Do Chaos Dwarfs actively engage in such conversion?
The answer, afaik, is basically no.
In old, old fluff, there were a number of “traitor” Dwarfs in the Chaos Dwarf ranks - the inventor of the Juggernaut Siege Tower (something Snakebeard) was an example, and Chaos Dwarfs actively tried to convert Western Dwarfs to Hashut/Khorne, often through torture.
However, in the current fluff, Chaos Dwarfs are an entirely separate culture. In the same way that an Imperial cannot become a Bretonnian, a Dwarf cannot become a Chaos Dwarf. Further, any Dwarfs that did turn to Chaos would likely worship one of the four Chaos Gods (probably not Tzeentch), leading them to join a Warriors of Chaos warband, rather than the Chaos Dwarfs.
In short, there’s a difference between Chaos Dwarfs and Dwarfs who worship Chaos, confusingly enough.
Imo Dwarfs are a separate racial group from Chaos Dwarfs. They share some common attributes like height, toughness, maybe some other race traits like stubborness and just being awesome at everything.
As far as I know there has not been any fluff in recent years of Dwarfs turning to chaos, but that does not mean it couldn’t happen.
I doubt either group would want to accept the renegades, but there might be small cults or clans where they are mixed together, but these would not be part of either society (they would live out in the wilderness somewhere).
I will make the point that the Chaos Dwarfs are the GOOD guys, and the Western Dwarfs are bad. They abandoned the Chaos Dwarfs to their fate, and went so far as to try and delete them from history!
I would have to agree they would be far more likely to join a Warriors of Chaos band for it’d be more likely they’d turn to the main 4 Chaos gods. That, and the northern wastes are probably easier for them to get to. Though I could see the Chaos Dwarfs having no qualms with trading with such Dwarfs…
The renegades in the North are just that - renegades. The Dawi Zharr are likely to view them as untrustworthy and have as little to do with them as possible. There is still that underlying Dawi psychology to deal with, and oaths are still highly regarded - so anyone who has abandoned their kin and the ancestors (the Dawi Zharr view themselves as having been abandoned by the Western Dawi and the Ancestor gods, so they have kept faith) would not be viewed as someone to bring into the fold.
although it might be interesting if the Dawi Zharr would start capturing younger western Dwarfs and turning them into something like the Jannissaries.