I have a classic car with some minor surface rust only, and one rusted out quarter panel. If I store this car outdoors under a tarp for 5 years, will the rust get any worse if it is kept dry? In other words, does rust continue to grow even without moisture?

I am wondering if I should get rid of the rust first, cover with primer, and then store it. I'm afraid I will worry about it outside too much unless I understand more about rust! Thanks...