"Stain" was your word, not mine. As a newbie, you're excused for using the wrong terminology, but even manufacturers and 'experts' can't seem to agree on finish nomenclature, so don't even try. Pigmented or not, you should avoid getting any of it on glued surfaces, but you state positively that no glue will be used to make this bed frame. Umm, I can't really picture how that can be, but You do You and note my tag line.

Your only question is about applying a second coat over a first. There should be no problem using the same product- especially if there's no pigment involved, but you'll be the first to know for sure. I strongly urge you to do some tests with scrap.