In theory as long as the game uses only the set of .Net APIs that exist in the 360 assemblies they should run on the 360.
I know people have compiled C++ (as long as they use the /safe flag) and Chrome (a pascal variant) so there is a good chance. See Other Languages FAQ
However be careful that Boo doesn't have any runtime libraries of its own as they may not run. e.g. VB.Net has own extra runtimes that people often assume are part of the language or .Net - they don't work on the 360 unless you are careful to avoid those things (e.g. the My. namespace)
You can deploy to the xbox wihtout using C# express if you use the command line packer tool (though you have to install C# express and GSe to get the DLLs and tools).
Let us know if it works...
The ZBuffer - News and information for XNA and Managed DirectX