Cimmerian Hegemony over Lydia and Phygria

The Cimmerians were a large tribe of Nomadic horsemen that ravaged Anatolia, taking both Phygria and Lydia. However, they were beaten back by Alyattes, and a plague damaged their foothold on the region.

Assuming Alyattes was defeated and killed, and the pleague was avoided, could the Cimmerians keep control of Phygria and Lydia, and expand their rule into Ionia? I need this for a timeline I'm working on(and I won't be randomly stopping).
 
To add on, is there any way the Cimmerians would have settled down and be able to control a large stable state in the area? And perhaps assimilate into a mix of Greek and Phygrian/Lydian culture?
 
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