Yes, a MAC can of course have an all zero result. But that doesn't matter, because the chance of that happening should be the same as taking a random choice out of a set where each element has the same probability, i.e. has a uniform distribution.
So the chance of an all zero popping up should - in this case - be about $1$ in $2^{128}$, assuming of course that the message changes every time (without pre-knowledge the chance would be the same, but identical input will of course result in identical MAC-values, so there's that). Now that is the same chance of guessing an AES-128 key in one go, i.e. the chance that it will happen is negligible. So in practice your scheme could be used fine.
Remind yourself though that using magical values should be avoided as a general principle. Even worse is of course that you remove all security provided by the MAC if the message is not encrypted. The integrity and authenticity provided by the MAC have value for unencrypted messages as well.
So yeah, you could certainly use the scheme, but I would rather sacrifice any other bit for this. I would not call it good practice. I'd only use the scheme if there was no other bit to sacrifice (i.e. the protocol is already established and I now have to perform a hack to put in extra options).
[EDIT] Note that an adversary in a scheme with optional MAC can send you any (unencrypted) message. Generally we require a MAC to avoid that situation.