Not if you only have one coop/run/tractor. Should be kept separate. In theory, you can brood them together and separate when the size difference is significant. The CX will outgrow and out compete the others. This leads to the CX abusing the others. Chickens are bullies and size matters. I wanted to do this until the details became clear. Given enough area and feeders, it should work. The key is enough area. If high density food production is goal, this won't work.
The Barred Rocks were very tasty. My experiment is getting CX to eat grass to try the flavor. They still go over the top on the prepared feed. But maybe it's enough for flavor.
I'm trying it and encourage you to try it too. I'll be waiting to hear back.