I think it will be fine. That's exactly what most artists keep their works on paper in. I think Jeff's problem is with the mat boards. Acid free does not mean 100% rag paper, nor does it even mean totally acid free. It can often still have a high PH rating and be given a rating of acid free. Quite confusing, but the easiest solution is to never buy any paper or mat boards that are not 100% cotton rag.
Acid free paper is made from wood pulp, not cotton. Often the mat boards are made from sandwiched construction w/ the outside of the mat board, the side that would touch the art work, being acid free. The other side is often laid on top of a piece of non acid free paper in the middle. The chemicals and acids in the interior part of the paper WILL leach out to the other side over time and onto the art work. Never use any mat board that is not made from 100% rag. It's more expensive and a little harder to hand cut, but it's worth it. Foam board presents the same problem if you are mounting your work to it unless you seal things w/ acrylic gesso before mounting the print. The fiber print itself is no longer made from 100% rag, but is coated with barium and a salt called strontium to insulate the image from the paper itself, and usually a hard gelatin coating over the emulsion, which performs a similar function of sealing papers with gesso, but of course it's translucent. Bromoil papers do not have the gelatin coating.
I'm in Florida too, which presents the added issue of humidity. Make sure to use packets of silica gel in the file drawers, and every now and then pull the prints out and rotate them in their order. A few times a year is usually sufficient. It would be best to keep a room dehumidifier near the prints in high humidity climates as well. No matter what you do, to my mind, the use of optical brighteners like barium, and the gelatin emulsion itself, mean that no photographic paper is truly archival like an art print, such as an etching.