I've fished the Harpeth for smallies a lot in the last five years, although I occasinally end up with more spots, largemouths, rock bass, white bass, or crappie. I normally don't like the idea of stocking trout in every possible stream, but I think it is a great idea in this case. The Harpeth is a nice river to be so close to Nashville, but has had problems in the past, like Franklin dumping a bunch of sewage in there when it storms. The trout stocking will draw attention to the river, and hopefully keep it cleaner. I hope all the rich -- um I mean influential -- Trout Unlimited guys around this area will feel a greater need to keep their thumbs on the people who affect water quality. There are about 1 million people in Nashville and the surrounding counties, and the trout fishermanwho have had to drive an hour or two to get to trout, and this will definitely catch their eyes.
Also, 10-inch trout make good food for magnum largemouths.
And I actually caught a pretty nice channel cat 2 weeks ago in there on a woolly bugger.
Attempting to answer your questions, I see no reason that the trout won't thrive until about May, when every last survivor will cook to death. As for a fly to use... I think that won't matter much. I think the biggest trick will be to find their haunts. Any fly is going to work for them, especially stuff like san juan worms, and wooly buggers, and gnats.
Although I think that they will draw angler attention, the Harpeth is LARGE, and the question about whether or not they will be fished out really depends on how many places along the length of it that they stock. If it is just that area west of Franklin, then I think that they may spread out so much (especially downstream) that they become scarce from that, and not the fishing pressure. I think that knowledge of where the hatchery truck dumps will be extremely valuable.