I believe you cannot do this without Outlook client as per Jukka.
Without the CRM Outlook client you can’t get the information into CRM without copy-pasting it from one window to another in the aforementioned scenarios. No synchronization technology will help you here, since CRM is unaware of the item until it has been brought into its world. The “Track” button is a client-side feature that you can’t utilize with any server-side solution, which means there’s no way for a user to select an email, appointment, task or contact from the Exchange server that he or she would like to promote into a record in CRM. Since the the record wasn’t “born in CRM”, it just can’t find its way there.
Last resort would be Smart matching with Tracking token, which may help you in this scenario.
Update:
Customer reply is going to reach CRM through a monitored queue. You can read a lot & get clarity from the above link.
Deploying a solution like the CRM 2013 the server-side synchronization will take care of moving items like calendar appointments and contacts back and forth between the end-user client device and the central CRM database, but it only applies to items that already exist in the realm of CRM. What I mean by this is that the item was either originally created directly in the CRM application or it was received via a monitored location like an email queue.
Your expectation is right, it should be tracked. I would open a ticket with MS & solve this.
Once the item is in CRM, server-side sync can take care of tracking the subsequent updates to it. A re-scheduled tracked appointment will get updated with the new date, regardless of whether you change the date via CRM or your mobile phone calendar that’s linked to Exchange. An email thread with a tracked message and a tracking token ID injected into the email subject line will have the next replies automatically synchronized into CRM