TL;DR No, you shouldn't block off or remove the vents. They serve a specific purpose.
Since this is an unheated area, any moisture which makes its way down there would stay there and cause problems. Mold growth would be promoted, and it could also prematurely rot the structure of your home. There would also be a foul smell which would be very hard to get rid of.
This area can still be used for storage, just make sure that whatever is down there is protected. Plastic storage bins are perfect for storing small items. You can also put up some hooks and shelving for other items. One thing you would want to avoid is storing anything directly on the concrete floor. You could put old palettes or pieces of wood on the floor. You also want to make sure that rodents cannot get in through the vents. You can install a piece of wire mesh over them on the inside to prevent them from entering. Just make sure that the mesh is going to be strong enough to prevent them from chewing through it or pushing past it.
This space would also make a perfect root cellar. There are some plans online here which will give you tips on how to do it. http://www.almanac.com/root-cellar-build