Tell us about yourself!
I build cigar box guitars with laminated necks made from scrap construction grade 3/4" plywood. I have done them both with and without an added fretboard. An even easier way to add a truss rod, without routing, is to simply laminate 3 pieces of plywood together lengthwise, so that you form 3 sides of a long box. The middle piece is only half, say, the thickness of the outside two pieces. I usually keep some 1/2" and 1/4" ply around for this purpose, depending on how wide I need the neck to be for 3, 4 or 6 strings.