Does the compiler discard empty methods?

Would C# compiler optimize empty void methods away?

No. They could still be accessed via reflection, so it's important that the method itself stays.

Any call sites are likely to include the call as well - but the JIT may optimize them away. It's in a much better position to do so. It's basically a special case of inlining, where the inlined code is empty.

Note that if you call it on another object:

foo.DoNothing();

that's not a no-op, because it will check that foo is non-null.