Hi greyeagle,
Outlook Express isn't part of MS Office, so whether or not you have MS Office installed on another PC is not relevant. What does come with MS Office is an entirely different product named Outlook.

If you have Outlook Express configured to access an account with, say, gmail, you can configure it so that the emails on the gmail server are not deleted when they're downloaded. This will make them available to both PCs. Whether that means both PCs will be able to receive all the emails via Outlook Express, I can't say. What I can say is that neither PC will 'see' any emails sent from the other.

__________________
Cheers,
Paul Edstein
[Fmr MS MVP - Word]