I was in the same position as you, ie had savings that I could use for the Gap...
but wanted to apply for my Super as I was no longer working for health reasons (not related to obesity).
And I decided not to go ahead and submit my forms in the eventuality that if they did go and check - which I think they can do - I wouldn't want to be caught out!
So, for me, it was the fear of being caught out that stopped me doing it.
All the best!