Because you said the house is on pilings, it sounds like it was built to federal standards. You will need to find out if your storage area meets Federal Emergency Management Administration, (FEMA) guidelines in case the big storm comes and wipes it out, you want to be insured. Ask your Building Official.
If I understand you correctly, by weatherproofing you mean making a dry storage space under the deck.
I THINK this is what I would do.
I would build an independant shed type stoarge area under the deck for a variety of reasons.
When the day arrives that you need to rebuild/repair the deck, you will not be tearing apart your storage area.
Depending on the lay of the land, I would install a garage door on end and a 36" or larger door on the side. I would have plenty of outlets installed,(GFI the first in the run.), and lights.
But, I think the real key is what the Building Official tells you!