Sealing the entire piece in Plasti-dip, Flex Seal, or similar type rubber coatings should provide adequate water-proofing to the foam itself, however the paint (as well as any decals or other accessories added after sealing) will still potentially be susceptible to water damage. Two or three layers of clearcoat should help protect the paint. Be sure to look for "exterior" or "weatherproof" on the can, or ask someone knowledgeable whether or not the paint is made to withstand weather exposure, as there are clear-coats that aren't really designed to be anything more than mild dust and smudge shields.
The downside here is that you have to coat the entire surface, inside and out, to make it truly waterproof. If you just coat the outside, the water will soak into your clothing/undersuit, run down the inside of the armor, and soak into the foam from there. While EVA floor mats, as Arcanine pointed out, are typically designed to resist moisture, 1) much of that is in the outermost layer, so if the foam has been scuffed, sanded, or by any other means the surface has been broken, that will undermine the protective layer, and 2) this protection isn't so much "proofing" as it is "resistance," which means while it won't drink up moisture like a sponge, it can soak through and it was not intended for the foam to be submerged or exposed to prolonged periods of dampness. More or less it's designed so that if you spilled something on it you could just wipe it up without having to worry too much about lasting moisture damage or staining.
But if you're only wondering if your foam build will be safe if you get caught in the rain and it takes a few minutes to find shelter, it should hold up well enough but I would recommend drying it off at your earliest convenience, especially if the clothing underneath has gotten wet as well.