I cover. I recommend a tarp from Harbor Freight, as they are the least-expensive I have found. I have seen folks that get the Adco covers say they last two or three years. Pretty pricey for a few years, when a Harbor Freight tarp will last two years.
With the AC and roof vents, and especially if you have the covers over the vents that allow you to keep them open in the rain, there should be ample circulation between the tarp and the roof to avoid much condensation.
As said, there are many opinions regarding covering. In my mind, it helps keep the caulking from aging any faster than it already does.