You can, but its not supported by Cisco TAC. BUT.. it all depends. If the Exchange server is located offsite and the link say is a 100 meg or gig fiber connection a location 50 miles away, I think you will be fine, and TAC does not seem care then. To Unity, it is local. But if the Exchange server is 1000 miles away, and connected with some MPLS or hodgepodge network, Unity will work, but what will happen, the MWIs will come out of sync, voicemails may or may not get delivered in a timely fashion, playback issues, etc.
Basically, stick with locally and tell them the other solution is unsupported by Cisco. If they go ahead with the deployment, layout the risks and what they are responsibly for if it does not work.
Tough spot, but fallback on the Cisco TAC does not support remote Exchange (or hosted for that matter).