If Kirk knew it was not so, then I don't see why he would have posited it to the M5 in the first place
...Then again, blatantly lying to a computer is a Kirk trademark. And Kirk already was aware of the human qualities of the M5, and might have been in a process of frightening or angering the machine.
The outcome where M5 says "No, double dumbass, there are
survivors!" would not be bad, either, because Kirk could then press on with that and have M5 agree to leaving survivors on other ships as well whilst securing victory. From there on, it would be a short hop to having M5 agree to securing victory through negotiations, without any casualties.