I, too, was curious how dropbox versioning works with the Mac OS X Lion versioning feature. Here's a few things I've tried, with the dropbox binary as of today (1.2.49 for OS X)
I went into the TextEdit program (This is OS X Lion Versioning enabled app. Pages would be OS X Lion Versions enabled, however, Microsoft Word would not, as that would require significant changes to the program and MS has not been able to accomplish it thus far)
I created a TextEdit file in dropbox, and saved a few versions of it. When using the dropbox web interface, it appeared perfectly in sync with their versioning system.
I duplicated the file (Under OS X Lion versioning, this creates an independent copy, or "branch" of the document to work on) This did the exact same thing on dropbox and created a separate file with no versions.
I've been using computers since I was a kid, (I'm 26 years old now) and I've never had any sort of version-control on my local computer's filesystem itself (Windows, Mac Leopard and Snow Leopard, various Linuces and other Unices) so native versioning in the OS X Lion filesystem itself will be a significant paradigm shift for me to get straight in my head.
So, the long and short of it for the OP's scenario with the Air and the Mini, using Pages (OS X Lion Native) versioning with dropbox on both computers should work well and as expected. Good luck in your studies!
Oh, be sure to check out
http://www.dropbox.com/edu to use a .edu e-mail address to get double the referral space bonus for yourself and others you've referred for being a student.