mrkicker
Why not just have one server at office1 as the main mail server for the main domain for all 3 offices. The other two servers at office2 & office3 can be gateway servers but do not collect mail, give server 2 & 3 different (real at cost or free) domain names. File & print sharing is done locally.
Users at all 3 offices have secure IMAP accounts on the mail server at office1, and can see their mail wherever they are.
You will have sync mail traffic using your suggested method, so I don't see any great difference having IMAP traffic between office 2 & 3 and office1.
Configure IMAP just to read the headers and only download the message if required. The message will be in the local profile on Windows then in the event that the connection to the remote office is down.
Alternatively give each office a seperate domain name and forward mail for each domain from the main mail server at office1 to the respective server, using techniques as suggested by the vdomain panel from dungog ie mail for domain 1 processed locally, mail for domain2 delegeted to server2, mail for domain3 delegeted to server3.
Users can still read the mail on whichever server it is & wherever they are by setting up multiple secure IMAP accounts.
I have the old vdomain contrib if you want it, although dungog has withdrawn it for now as it needs more work, mentioned recently in the forums.