I don't believe the VM is aware of LINQ at all. As far as optimization, there's no guarantee to pureness with CLR code, so the compiler/JIT cannot do very much. (That is, a query composed of multiple parts cannot be turned into a nice simple loop.) The generated code creates enumerable objects, and possibly closure objects which are called via delegates.

On the topic of multiplatform, Mono has been working very well for many people. http://www.mono-project.com/