If you have 2 or more Queues with same Incoming email address and if one the the Queue is Inactive then one would expect CRM Server Side Synchronization to process the email and assign it to all the Active Queues for that email address.
However actually CRM Server Side Synchronization will not process such emails and not Email activity will be created.
On CRM Mailbox, ALERTS something like following will be captured.
If you look into Trace logs you will find error logged as
>Crm Exception: Message: You cannot add items to an inactive queue. Select another queue and try again., ErrorCode: -2147220190, InnerException: Microsoft.Crm.CrmException: You cannot add items to an inactive queue. Select another queue and try again.
Resolution for this problem is if you do not want to use the Inactive Queue, clear its Incoming Email value and deactivate it again.