There might be some concern of some of the soil's nitrogen being temporarily diverted by the bacteria that eat down the carbon sources, but I don't think a little bit of incompletely decomposed wood or cardboard in the soil should be a problem, unless your nitrogen is already badly depleted.

If it won't bother you it'll probably be good for the soil.

We're trying to grow some indoor veggies in coffee cans in an unfinished mix: potting soil, clay, unfinished outdoor non-worm compost, and unfinished indoor worm bin compost (roughly 13%, 26%, 56%, 4%, although the vermicompost proportion is probably a tiny bit higher since they've been mixed a couple weeks and a few live worms have still been working in there). Just put the seeds in tonight. We'll see how it goes. The stuff I have now, while not broken down thoroughly, looks a hell of a lot better than the native compacted red clay soil.