When q-call buttons are put on a SIPCC phone, they don't work as expected until an agent logs into the phone. The phone then subscribes to the avaya-cm-cc-info event package, which includes notifications for the q-call status.. This should be changed in CM so q-call buttons can function with the avaya-cm-feature-status subscription (and likewise work on a type "SIP" phone vs having the "SIPCC" requirement). Many call center supervisors don't handle agent calls.
Also note, upon agent logout from the SIPCC desk phone, the phone does not unsubscribe from the avaya-cm-cc-info event package. The q-calls buttons continue to work until the phone or CM are rebooted. That's probably a bug in the phone's firmware.