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[X-Men] What Would Happen if Rogue Drained Phoenix?

As I understand it, Jean  Grey/Hope/Rachel/Whoever channels a specific cosmic being, the Phoenix Entity, yes?  So... if Rogue were to drain that channeling ability, would they fight each other using the same being?  Is there any precedent for the Phoenix "rejecting" a call?  Or is it more a "Power Cosmic" type thing?  

Thanks!
gpt
So, the Phoenix is more of a "possession" than a "channelling" thing.

It, in and of itself, is a cosmic being, and a force of nature of near-endless power. Like, star-eating levels.

If Rogue were to drain someone capable of hosting the Phoenix, there would be no consequence in terms of the Phoenix. If Rogue were to attempt to drain someone possessed by the Phoenix, she would most likely be overloaded with minimal impact to the Phoenix.

It would be like trying to jump start a car directly off a substation.