When I put away my drill for storage, should I be concerned about whether the chuck is fully open, fully closed, or somewhere in between?
Doesn't make a major difference. The chuck is a rather precise thing and dust, sand and moisture which are all bad for the chuck will get into in regardless of how open it is.
Only one thing comes to mind: when the chuck is getting closed the jaws extend out of the chuck and so there's greater chance that they accidentally catch on something and scratch or damage that, but that's an unlikely edge case.
I'd say the most important thing is that once you open the chuck so such extent that the jaws don't extend from the chuck body anymore the chuck and the whole drill get shorter and that's quite useful both for storage and for transportation - takes less space in the bag, has less chances to scratch or pierce stuff. I've never faced any real problems because of having a drill chuck left in "wrong" position for storage.