Yes, this is very possible. There is already a version of mono designed to compile/run on the ARM processor and available for PDAs/Cell phones. I imagine it only provides a compact framework too, which should help out with some of the memory constraints and offloading unecessary assemblies (not sure on this though).
For more details:
http://www.mono-project.com/Mono:ARM
One issue though I could see is that pretty much all the graphical UI stuff done in mono is done through Gtk#, which is a gnome library. I don't imagine this comes with my iLiad, and these libraries could require a fair bit of storage again.
All in all though doesn't look like it would be too much work.