Cardboard does not conduct electricity
Which is why... it's NOT anti-static. Anti-static bags are conductive.
I don't know about cardboard, but I know that paper can build up a static charge. That's why they tell you, when re-loading a printer paper tray, to always take one end of the group of papers you are putting in, and flip through them, to dissipate any static that might have accumulated on the pages, and which is a source of paper mis-feeds / jams, when pages stick together due to static. At least, that's what I've been told.
That being said, the practical reality of things is, it probably won't hurt anything significantly in the long run, if you store a video card in a cardboard box.