When a first radio of a UE has an air-interface connection with an access node on a first carrier and the UE encounters a trigger for the UE to scan for and report to the access node coverage on a second carrier, a second radio of the UE, rather than the first radio of the UE, will conduct the scanning, and the first radio of the UE will then report to access node over the air-interface connection on the first carrier a result of the scanning conducted by the second radio. Optimally, the first radio of the UE thus need not tune away from its air-interface connection with the access node in order for the UE to scan for target coverage on the second carrier. And the process could thereby help avoid the interruption of communication between the UE and the access node on the air-interface connection over the first carrier.