At the the start of the Nomad turn, that player expends a Command Token to cancel the Possessed state of a TAG. The TAG in question is in base contact with a Combined Army trooper. My expected outcome here is that the two models are separated by a fraction and are not considered to be in the Engaged state. Is that correct? And if it's not correct, can either player decide they want to be in the Engaged state and thus force it to happen?
Engaged state will be automatic due to base contact. There's no choice involved. Note that it also works the other way - if you have a trooper in base contact with your own TAG, it will become Engaged as soon as it gets Possessed, which can be a good defence against having your own TAG shoot your other troops.