It should, but they've recently been somewhat picky about which phone numbers they accept for the initial setup.
Once you get it, you don't need access to that US number afterwards – very useful when traveling; everything just works via VoIP, including texting, which is a lifesaver for 2FA when traveling without US roaming.
Of course, it's a Google service, so expect it to be discontinued without warning at the exact moment you've totally integrated it into your daily life.
