DH and I tried this tonight. It was good, but I'm going to improve on it some more for next time.
Tonight I did add seasonings to the chicken and cooked the chicken without the garlic and peppers. I didn't want the pepper to be mush, and garlic can't handle that much heat without burning IMO. I cooked the chicken in a bit of extra virgin olive oil. Not a lot. Just enough. I added some season salt and chili pepper to the chicken too. Odd, but it did work quite well. I also used bow tie pasta instead because those bows make me happy. :D Last, I added lots of fresh ground pepper. Mmmmm.
Next time I make this I'm going to add one cut squash to the pot when I throw in the pasta. I'm also going to cook up half a chopped onion with the chicken. Other veggies might go well with this too. I will also use less cheese. It was way too cheesy for us, and we LOVE cheese. So I'm going to start with half the cheese and only add more if really needed.
This recipe was a good starting off point for a better meal though. And it only uses one pot, which makes my dish washer (DH) quite happy. :)