If it looks like black dirt because it has broken down (which may be the case since it's 2 years old), you can use it as a mulch or mix it in with your soil. If it looked that way from the start, I would only use it on top of the soil, since it needs nitrogen to break down. If you put it on top, it can get the nitrogen from the air, but if you mix it in, it'll get nitrogen from the soil.

I know of someone who incoporates composted wood chips into a very clayey vegertable garden and swears by its effectiveness. It would be better to use the wood chips in your compost but you could always try it. My inclination would be to leave a section untreated as a test bed to see how the veggies grow there. Once you have done that, you'll be the expert.

Testing it out is a good idea.
You can always just use it as mulch and top dress. You don't have to till anything in, it will still help by being on the surface. As noted eariler, if it is well broken down, then you can do whatever you like.

Any organic matter is okay to use in clay soils, or sandy soils. No matter which type of soil you have, even loam, it will be improved by the addition of organic matter. Whether the mix that into the soil or use it as a mulch depends, but even though that hardwood mulch is 2 years old I would only use it as a mulch and would not mix it into my soil, even with as active a Soil Food Web as I have.