Yes they have, and if Sheff Utd do the same then they would be another example. I would say that Norwich clearly had a policy which was do what you can in the prem your not getting much investment in players, so it would be difficult to lay the blame at Farke's door and so far he has had to stand losing some players and is doing OK back in the championship, but it hasn't stopped a board pulling the trigger on a manager before (lack of support that is).
I'd tke issue with Clough making some "great" signings, I struggle to think of one he made that I'd bestow that description but no doubt you might come up with a name that will change my mind!
What would have happened if he'd stayed? We'd have bumbled along in mid table, I mean he went to the Blades and hardly pulled up any trees there, back to Burton where admittedly he had limited resources and is now at Mansfield - a good manager to work within a budget and improve a team over time in the lower leagues IMO. Would he do better with a bigger budget? Not sure but it doesn't look as if he is going to get a chance.
After Clough well we became a top 8 side making a realistic challenge for promotion most seasons and on the odd occasion the football has been worth watching. I doubt that would ahve happened under him, but its not possible to prove that obviously.
Its difficult compare Derby with the clubs you mention, I mean there are some good sized clubs languishing in league 1 - Sunderland and Ipswich being but two examples. Wolves are a unique case in that they were big decades ago and a change of ownership has pumped money into the club, together with a clear strategy, involving player recruitment, a top class manager and the involvement of an agent. Leicester have never been "big" but again have had a change of ownership and money pumped in with a clear strategy for success. Maybe its our turn next?