Not. The CLR is user mode dependent and cannot be hosted in kernel mode.
However, there are two more questions: one, that if you somehow satisfy the CLR dependencies, for example, by providing your own implementations of Kernel32 and User32 and other user-mode components, then this is probably no less possible. Secondly, the language itself can be used to output some other language, such as the x86 assembly, where possible. You will need to write a translator and provide analogues like BCL, however.