Yes, I was asked about family (I had wife/kids). Or I may have brought it up.
Anyway I told them the truth, that i had a partner and she was supportive. I don't think being in a relationship (or not) affects your suitability for training.
Whatever your situation, just be honest. If you try to fool them, you are really just fooling yourself and setting your self up for a fall. Recruitment is stringent because the training is tough and NATS know what they are looking for and have a good reason for the criteria