Ymgarl Genestealers seem to be the first Tyranid life encountered by the Imperium, and quite a while before. They were believed to be a native life form of the moon Ymgarl.
Tyranids take their name from the Tyran System, where the first Hive Fleet properly arrived/was noticed/documented.
In theory, there’s nothing to prevent Ymgarl Genestealers from beginning a Cult.
That being said, the Hive Fleets themselves show no interest in reabsorbing Ymgarl broods. Indeed they’ll go to some effort to avoid just that. Why remains an open question, but the lore theory is something to do with their unstable genetics.
Now. That Ymgarl Genestealers have spread beyond Ymgarl is highly suggestive they can do what all other Genestealers can do, but I’m not personally aware of specific examples.
It could also be argued the Ymgarl are just an expression of an underlying genetic quirk of all Genestealers. If so, what are called Ymgarl Genestealers could just be a widespread genetic variant any and all Broods could come to express.
Now. Onto Cult Structure.
The Magus does have autonomy. As do most if not all members of the Brood. However, the Patriarch can still override that via the Broodmind as and when necessary.
As for establishing a Cult? There is by no means just a single Purestrain involved. Indeed it would be in the nascent Cult’s interest to get as many Purestrain planetside as they can get away with. Not only are they useful bodyguards for the new Patrirach, but they’re also redundancy in waiting should the Patriarch be slain.
Hive Fleet Tiamat I’m afraid I don’t know much about, so shan’t comment