To answer your question, yes it will work. Use the sharpest cheddar you can find, and grate it with the smallest holes on your grater. That will make it easier to melt into the pasta. Also, using an easy melting cheese, like butterkase, or fontina will help make the mac & cheese more creamy. Adding finely grated mozarella or provolone with give it some stretch, if you like strings of cheese stretching from your fork.
Also, a little Parmesano Regiano, or Asiago will add a little salty bite to the dish. And if you like it, by all means, add a little American cheese, or Velveeta, again to mkae it more creamy.
I disagree with cooking it after the cheese is added as you can easily overheat the dish, causing the integrated sauce to break and become clumpy.
Using a roux or not is completely up to you. I've made mac & cheese both with and without a roux. Both taste great, depending on my mood.
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