I would say that strong AI could appear sooner than otherwise with faster hardware. This is because, the earliest algorithms for strong AI are likely to be flawed and imperfect. These imperfections can be compensated for by faster processing. Think of the earlier chess playing algorithms. Although Deep Blue was able to defeat Gary Kasparov, the algorithms themselves were relatively primitive compared to modern chess playing algorithms; although they achieved their goals, they did it with more computation than was necessary due to the algorithms being more brute-force orientated. As the algorithms got more sophisticated, the computational hardware needs decreased.
Faster hardware also allows you to get by without fully understanding how the strong AI algorithms work by using evolutionary methods. You use brute force evolution to evolve algorithms that are even more efficient than their parents. Some people might frown upon using evolution to create AI but that's what was used to create human intelligence so why not use evolution guided by humans to create machine intelligence?
You make an excellent point about how early imperfections in the algorithms could be fixed as they evolve through feedback, and that this step-process running faster would get us the desired (evolved) algorithms quicker.
But couldn't we accomplish this with distributed processing rather than faster hardware?
I think distributed processing is another form of faster hardware. It is certainly more operations per unit time. Evolutionary algorithms are interesting because they are able to exploit parallel processing better than most. Evolution amounts to a type of heuristic tree search, where once an algorithm has found a solution to a problem, the knowledge is persisted and shared with other algorithms.
Later algorithms can be run on lesser hardware because they don't have to retread the same territory as their ancestors; they only have to search the space that hasn't already been examined. As the saying goes, they search "smarter, not harder".
Faster hardware also allows you to get by without fully understanding how the strong AI algorithms work by using evolutionary methods. You use brute force evolution to evolve algorithms that are even more efficient than their parents. Some people might frown upon using evolution to create AI but that's what was used to create human intelligence so why not use evolution guided by humans to create machine intelligence?