Is it possible to run (develop and/or deploy) Rails applications without rubygems?
Yes and no: you'll need ruby gems to install the code, but you don't need use the 'gem' tool hitting the rubygems server to do it.
To make a long story short, if I'm in an environment without 'net
access and without rubygems, am I out of luck with respect to writing
Ruby on Rails applications?
If you can figure out what all the gems you need are, you can manually download them (with a web browser or wget or what have you) to local media, somehow get that onto a machine in the net-less environment (burn a cd from a machine with net access?) and then install there using the gem tool (which you'll also need to have grabbed beforehand).
You might want to try installing rails on a machine with net access first just to get the list of all the gems you'll need to actually get an instance up and running.