QCS appears to be functional but no messages are received from the partner. "Test Mailbox" works and MFCMAPI is able to log into QCS service mailbox. However "Total messages received" always reports zero.
Upon the more detailed investigation it was discovered that all arrived messages are instantaneously disappearing from QCS service mailbox even though all QCS services were set to disabled. This happens because mailbox calendaring settings are set to AutoAccept like for the resource mailboxes instead of AutoUpdate. The following PowerShell commandlets need to be executed on Ex 2007:
get-mailboxcalendarsettings name-of-service-account | fl automateprocessing
(Look for AutoAccept, or anything other than AutoUpdate)
set-mailboxcalendarsettings name-of-service-account -automateprocessing AutoUpdate