There are essentially two methods to get what you want, and you can use them separately or together:
Saturated Fat
Butter and other saturated fats (i.e. bacon fat or even chicken fat) will do wonders to "bind" sauces to chicken. Among other reasons, it's partly because saturated fat is solid at room temperature and still fairly viscous at moderately higher temperatures.
In fact, traditional "wing sauce" is invariably some combination of hot sauce and butter. The butter helps cut the spiciness and also helps keep the sauce attached to the meat.
Dry Heat
I use this technique for ribs far more often than chicken, but the idea here is to make the sauce into a glaze by reducing it.
Set your oven to broil and apply a thin coat of sauce to the meat; make sure you cover it completely but don't glob it on. Now put the meat on a rack beneath the broiler and wait until you see the sauce starting to bubble (should be no more than 1-2 minutes if you've applied enough sauce and your oven is hot enough). Then take it out of the oven. Repeat several times until you've got a thick, sticky coat of sauce (usually around 5 times for me).
Note that if the sauce is very thick (i.e. a store-bought BBQ sauce) then you'll actually want to water it down a bit first.
For chicken I honestly prefer to just throw in some butter, but you can use either technique as long as the meat isn't too lean.
As the others have mentioned, it won't quite be the same ... however, it can be done, it just won't quite have the same flavor as there isn't a chance for the meat juices to transfer into the sauce, and some issues regarding mixing it back in with the cold pasta.
If I were going to try it, I'd brown the meat, remove some of the fat if it's a really fatty grind, then add some extra sauce (or even other liquid ... maybe dairy, for a classic bolognese) to let it simmer for a bit ... then toss the pasta in with it to reheat.
The extra sauce is the key, otherwise, the meat isn't going to blend in with sauce on the pasta, If you reheat the pasta in the fresh sauce, it should hopefully mix together more completely.
... but if I were to do it, and wanted to add a meat to an already cooked pasta, I'd probably not choose ground beef as a first choice; I'd probably cook up some sausages, cut it down to an appropriate size for the pasta you're dealing with, and mix that in, possibly adding some extra liquid when reheating the pasta.
Best Answer
Learning how to season with salt (especially) when cooking is what separates good cooks from those who are not as accomplished. Yes, you should season the chicken, whether or not is has an accompanying sauce. With attention and experience you will learn how to adjust that seasoning depending on the seasoning of other ingredients in the final dish. However, you should season each component to some degree (again, salt specifically...other spices as needed).