Specifically, if I were to buy a male puppy from a responsible breeder with good lineage and get him titled through Sch1 or 2 (or go all the way 3), would a responsible breeder be interested in using him, and does the breeder approach the owner or the other way around?
There are so many variables, it's hard to say.
Let's say for the sake of argument that you get your hands on a dog whose bloodlines are valuable and sought after, has a fantastic temperament, conformation, and excellent working ability, you title him to SchH3 and get a V and kkl1 in conformation.
If he is truly a breedworthy specimen, you may find some of the people in your club are interested in breeding to him. If word of your dog gets around the GSD community, bitch owners would be contacting you if they are interested in breeding. You might buy a print ad in SchH USA or other publication announcing your male is available for stud, if you really wanted to campaign him, but most of your advertising is going to be word of mouth from people who have seen your dog work.
Now, on the other hand... let's say you get a male with very common bloodlines that are available just about everywhere, you title him to SchH2, and he gets an SG kkl2 in conformation. He may be the best dog in the world for you, but he may not get much attention from breeders because there are so many of his kind out there, and since bitch owners can take their pick of studs they are going to want the very best that they can get. Your dog would probably be overlooked by all except backyard breeders in your neighborhood.
But like I said, there are so many variables that it's hard to speculate. At the point of a beginner, I would never count on raising a dog FOR stud. You get your well-bred dog, do everything you can to acheive your goals with him, have fun and learn a lot... but unless he is really exceptional you probably shouldn't count on getting stud fees. If it happens, it's icing on the cake.