Hello Foodkop, Considering it will be located in a closet of the bathroom, there shouldn't be too much problem with moisture. I would suggest though that if you plan to cut it down for use as shelves or the like that you trim the cut edges with a veneer. This will help protect and seal the wood away from moisture. I've included a link to the edging below. I hope this helps. Cheers, Chris Melamine Edging: http://www.homedepot.com/s/melamine+edging?NCNI-5
While I don't have experience with this particular product, every melamine coated panel I've ever seen had an MDF core. I'd bet you 100:1 odds this one was the same.
Edge banded means that the veneer is also applied to the edges of the sheet as well as the top. So if you don't cut into it, the whole thing will look like it's made of the melamine material.