Is it possible to create a shared backend logic using .NET and have the respective GUI front ends in MonoTouch and MonoDroid?
Yes, with some limitations due to the way MonoTouch works. Apple do not allow running of any background VM or service in order to JIT compile CLR applications, so all MonoTouch applications are AOT compiled, resulting in loss of dynamic abilities and reflection. The link will detail what is missing, and there's another link in there showing which libraries are available to MonoTouch apps.
MonoDroid does not suffer the same limitations because Android can run the full VM. So if you need to share a library between the two, you should build the library using the MonoTouch capabilities, and keep any dynamic related code in the MonoDroid projects only.