Would any of you know if the following scenario is "doable"?

We run an old Exchange 2010 infrastructure at my work, and there is no way they are going to spring for newer: getting them to go from 2003 to 2010 was an ordeal... 

Could I set up an Ubuntu Postfix "relay" server between Exchange and the Internet, that also permits one particular mailbox to be accessible from a Dovecot install on the same server (as well as relaying the mail for that mailbox to Exchange)?

Yes/no and pointers most welcomed.