I installed the distribution (for Appstore) provisioning profile in Xcode, but it doesn’t show up under Devices, only the Developer provisioning profile shows up. I cannot “Build and Go” with the distribution provisioning profile in Xcode either, however, “Build” does work.
Is this the correct behavior?
That’s right. You can only use this profile to build App Store builds. For your testing you need a development profile. The distribution provisioning profile has nothing to do with the devices you registered on the iPhone development site.