You need to scrap this solution entirely.
Reconfigure Outlook as a MAPI Exchange client, which is the way that it was intended to be used. Doing so will enable the office to take advantage of the rich e-mail and collaboration features and functionality built into Exchange and Outlook. You already own it, so you might as use it.
You are using Outlook 2003 which can be configured to use cached mode which will create an offline storage (.OST) file, allowing users to access their mailbox when disconnected from the network. The best part about this is that all data is preserved on the server which makes it easy to manage and back up; also, all changes made while offline are synchronized with the server when users connect to the network.
I understand the desire to go green, if you will, but the power draw from turning on the servers in the morning in all actuality probably cancels any energy and cost savings throughout the night. It’s also important to consider that turning the servers on and off shortens the life span of its electrical components resulting from constant expansion and contraction.
Choosing to leave the servers on also opens up additional options such as deploying OWA which is installed and enabled for all users by default; however, it should be deployed with SSL to prevent data, including user names and passwords from being transmitted “in the clear”. There is also RPC/HTTP(S) which enables users to use the full MAPI Outlook client over the Internet without first having to establish a VPN session.
.PST files have limitations associated with them such as being prone to corruption as they grow larger in size. You mention having to back up each file manually and the notion may be to store them on the network but that would make them inaccessible in the event that users are disconnected from the network; the files themselves are also not designed to support network input/output but file system input/output instead which can result in degraded performance and crashes for file servers.