Of course you could, but hard wood is, well, hard. The cells are tight and it is not as absorbent as soft pine. Hardwood chips do not decay very quickly if your goal is to compost the litter when you are finished. So...... it's you call.
There is a higher risk of problems relating to Aspergillosis when using hardwoods. Aspergillosis spores are present pretty much everywhere, it's just that hardwoods can promote the growth of it in great amounts, and so the risk is elevated. It is up to you if the risk is worth it or not (everything we do has minor to major calculated risks!). Note that it is generally believed that hardwoods that are not kiln dried are a much higher risk. Of course, no matter what the bedding is, keeping it dry helps to reduce spores of any type!