Can I declare main as void, to shut off these annoying ``main returns no value'' messages?

No. main must be declared as returning an int, and as taking either zero or two arguments, of the appropriate types. If you're calling exit() but still getting warnings, you may have to insert a redundant return statement (or use some kind of ``not reached'' directive, if available).
Declaring a function as void does not merely shut off or rearrange warnings: it may also result in a different function call/return sequence, incompatible with what the caller (in main's case, the C run-time startup code) expects. That is, if the calling sequences for void- and int-valued functions differ, the startup code is going to be calling main using specifically the int-valued conventions, and if main has been improperly declared as void, it may not work.
(Note that this discussion of main pertains only to ``hosted'' implementations; none of it applies to ``freestanding'' implementations, which may not even have main. However, freestanding implementations are comparatively rare, and if you're using one, you probably know it. If you've never heard of the distinction, you're probably using a hosted implementation, and the above rules apply.)