If you like to add Parmesan cheese to your spaghetti or other pasta dishes, add the cheese to the pasta and mix well before adding sauce. The sauce will cling better to the pasta that way.
The only time one does not rinse the starch off pasta is when it will have spaghetti sauce added, as the starch helps the sauce stick also. I have done this for a long time (your idea) as well as adding some butter or oleo first before the cheese and then the sauce. It tastes really nummy. Have you tried pasta plain with butter and parmesan cheese?