It's cardboard, and a lot of people use cardboard boxes as mulch, so I don't see what it would hurt. It would break down by next year, and you could till it in. Any organic matter is good for clay soil, so it would be a nice, frugal way to get some. Go for it!

With the sod on top of them I don't really see how they are acting as mulch. I just soak mine, tear them up and put them in the compost pile.

I have found they dry out quickly. Maybe shred them up and put around plants.

We are saving ours for fireplace starters next fall. We will put a pine cone in each egg spot, pour wax over them. Hopefully we can break them up and use for fire starters. My mom and I did this years ago and even had a powder to sprinkle over the wet wax that cause the fire to look different color when it was first lit.

Gloria