No, this is not possible. When a new mail arrived at the maileater, it just replies onle the Success or the Failure message.
At this stage the Incident or Request is not yet created, so ServiceDesk cannot reply with the Incident or Request number.
But "one second" later, the Initial Notification is triggered. And this Notification contains the Incident number in the subject line, so the user can reply directly to this Notification.