The cardboard dulcimers I've seen have been decent starter instruments. The sound quality isn't as nice as a wooden dulcimer, but it isn't near as poor as we might expect. They are pretty cheap to start with, but I believe some assembly is required. Not much, essentially you glue the fret board to the box, and install the tuners & strings. As long as the frets, nut and bridge are accurately placed in the fret board, and the nut & bridge height is set correctly,they play in tune and play easily. If you decide you want a better instrument later, you will have some playing skills to help you choose your next dulcimer. If you decide dulcimers aren't for you, you won't be out much money, and can pass the cardboard model to someone else to try. If you decide to keep playing, you also have the option of building a dulcimer, using the fretboard from the cardboard one. The fretboard on cardboard dulcimers is not cardboard, it's always wood. Talk to the local builder, and have him explain some of the terms I used here, and how the height of the nut and bridge make a difference.
There are also some builders making inexpensive wooden beginner models. Dave Lynch, of Sweet Woods Instruments builds a Student model from plywood for a very reasonable price. http://www.strothers.com/sweetwoodsinstruments.com/index.html You may find the price difference between the cardboard and Dave'sStudent model isn't a very great expense. I believe some other makers also have beginner models. The cardboard ones are unlikely to have much resale value if you decide to sell it, where a wooden one will retain more of it's original price.
Paul