>(a) there exists a C-preprocessor instruction as per the above

There's no day-of-week but you could cause mayhem with __DATE__

>(2) if the compiler will notice errors in the unexecuted branch of an #if

Compiler only gets to see preprocessor output, it won't.

>if printf; would give a syntax error

Perhaps surprisingly but no, it's just statement without effect (containing expression returning function pointer to printf).