For this to work in Qualcomm's favour, they would need to be given access to X86 first and foremost. The "client division" from Intel would be just getting a few engineers, marketing, sales and some managerial level to link it all, but without key access to their technology it wouldn't work as plainly described. Also, correct me if I'm wrong, but don't AMD and even VIA have a say on who can get X86 stll? Specially AMD thanks to the X86-64 extensions. While AMD doesn't seem to be in an adversarial relationship with Qualcomm, I don't know if they'd want Qualcomm as a direct competitor to them. At least not right away in the consumer space for X86? They did sell part of the ATI portfolio to get some cash back to them, so they do have a history, but that's as far as I know.
This is not like IBM selling off their client division to Compaq and later Lenovo, since IBM was only designing full solutions using external parts.
I have trouble seeing what Qualcomm would get out of this?
Maybe there is* information or context missing and my interpretation of this is skewed the wrong way.
Regards.