So Mulberry is a remarkably feature-rich Apache-licensed email, contacts, and calendar client I'd never heard of before I looked through a list guinness posted almost a year ago. A PortableApps thread pointed to instructions to make portable.
Download
http://www.mulberrymail.com/download.shtml
How to make portable (for Windows and Linux)
http://trac.mulberrymail.com/mulberry/wiki/usbkey
Will test hopefully in the next few days.
Edit: Sadly, I couldn't get it to download Gmail, even with a lot of tweaking. It hasn't been updated in almost 4 years so I think I'll let this one go.