Sure there is a chance for you to win without deposit as you can participate on it freely with the free tickets. It is proven already as there were some winners with so low numbers of ticket like 1-100 tickets which I believe all of it were free tickets from the free roll.
Why you need to be afraid of it if you do not want to deposit? Even if what you say is true, then there is no need to be afraid as you wont lose anything except your time you spend to claim the free tickets.