You will probably lose complete functionality. Google Edition isn't available on CDMA. So flashing that ROM is like breaking the rule of don't flash ROMs that are not your carrier.
Actually I'm pretty sure HTC sells the one as one phone, the same across all carriers (both hardware and software wise, prior to activation). It carries all of the bands to work on gsm networks. The problem being is that, you would have to have it unlocked from Sprint for domestic use. Of which they are currently refusing to do.
When you first get the one from sprint, the activation code you enter, or the rep enters, not only activates the phone. It also downloads a sprint configuration pack, installs it, and locks the phone to sprint only. After having your account in good standing for 90 days after your date of purchase, they will unlock the phone for international use, if you ask. However they will straight out refuse to unlock it for domestic use, and so will HTC as it has to be your carrier that unlocks it.
So theoretically speaking, if you buy the phone from sprints website. As long as you don't activate it, you should be able to use it on any network, given you have the sim, as I'm pretty sure they are sold sim unlocked. It is only when you enter a carriers activation code, that it locks the phone to that carrier.
Going back to the ops request, you should be able to flash it. But seeing as how your most likely sim locked to sprint. You won't have any service, probably not even roaming. The only thing you'll be able to do is use WiFi messaging with a VoIP app for calls.
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