Well, you can leave it outside but I suspect that won't be good for the rods. They'll more than likely continue to rust further. The only thing I can suggest for that is to apply a liberal amount of marine grease to them to prevent further rust. But bear in mind that grease (being a petroleum based product) will likely wear out the plastic bearings in time. If you can find a heavy duty silicone based grease, that would be best.
From what I know of FAS, it might be slightly difficult to put in a laminate instead of paper pitch because the gap between the underlying board and the glass pitch is tight, especially built for a paper pitch. If you can find a VERY thin laminate then that might work. If it were me, I would get the laminate of your choice THEN buy marine plyboard to replace the chipboard board under the glass. The width of the laminate plus the new plyboard should equal the width of the original chipboard. Plyboard will be able to withstand the damp of the outdoors much better than chipboard, which will likely warp in time. It should be an easy fix and the plyboard along with the grease should make your table last longer outside.