Credit goes to Kevin McMullens for answering my question:
Yes, you can migrate your Unity VM version 3.1(3) from your Dell Server to the ICS 7750. We used a subset of the original Unity 3.1(3) CDs for our ICS Unity 3.1(3) product. Basically, we removed the OS CDs, since the ICS 7750 has it's own SPE Win2k CD. We also removed the final CD from the set, I believe, which contained Dialogic drivers which we don't need on the ICS 7750. Otherwise, the CD's are the same. If you'll go to the http://www.cisco.com/univercd/cc/td/doc/product/voice/ics/icsapps/icsunity/index.htm web page, you'll find the pdf file for the Cisco Unity Voice Messaging 3.1(3) for the ICS 7750 doc. That should take you through the reinstallation. If you're migrating data, you'll need to use the DiRT utility to back up the voice messages and then reload them on the SPE after you've done a fresh install of Unity on the SPE.
Your dongle should work as is, however, it would be good to update the information in the dongle database to reflect that it's now running on an SPE.