You can do it if you want, but it will be a mess of trouble.
My suggestion is to find free wood. Look through Craigslist (in the free stuff section) and you will find plenty of people throwing out furniture like old desks and whatnot. There's your free wood.
My main apprehension against cardboard (besides fungus and toxic death to your plants) is that hanging enough lights above the plant to grow anything worthwhile will cave in cdboard after a while, even good cardboard.
But hey, where there's a will, there's a way.