Can I compile .NET C# code on my Mac?
You can compile C# code yes.
I would rather not install Parallels and Windows if I can find a way
to cross compile this without needing that heavy of an installation of
Mono does not have 100% compatibility with the .NET implementation.
The Common Language Infrastructure (CLI) is a framework for executing managed code. The CLI consists of several parts including a Virtual Execution System (VES). .NET's VES is the Common language Runtime. Mono has it's own separate VES implementation.
In other words, at the very least do not expect to run code that has only been tested in a *nix/OSX environment to run without testing it on a windows environment.