You do not need a link to the internet. You just need an active link.
If you have an existing IAP that is up and running it is what we call the "Virtual Controller" (VC). The VC owns the IAP network. Any IAP you connect to the network in the same vlan as an active VC will get a copy of the config from the VC. As such, the new IAP will never advertise the "Instant" SSID. Your issue likely stems from the fact that the active VC is running an older version of code. The VC manages the version of SW across all members of the group and will even downgrade code on new members so they match the version running on the VC. v. 6.1.3.4_3.1.x.x is required for the RAP-3. If your active VC has an older version then your RAP-3 will not boot correctly.
Having said that, having connectivity to the internet makes doing SW upgrades easy as we host SW upgrades in the "Cloud" and all you have to do is hit the "Check for SW Upgrade" button in the WebUI under Maintenance.