The above is correct but if you were to say something like 'she left without him', it would not work; 'she left with no him' does not make sense.
Generally, just do not use 'with no' when talking about people, or specific animals (e.g. 'she left without her pet' =/= 'she left with no pet'. Both sentences means she left without an animal however the first tells us that she left without *her pet*. The latter implies that she left without *anyone's pet*)