Is it fair to say Herbert Hoover was simply unlucky to be the president at the wrong time, during the Great Depression?

Yes, I would say there is justice in the remark that Hoover was unlucky in his timing. By all reports, he was a decent human being, raised as a Quaker and known for his humanitarian work. He was also a more-than-competent businessman. His character was good, and he didn't want people to suffer.
The Great Depression caught Hoover by surprise. He was an optimist who believed in business, the stock market, and capitalism, and he couldn't truly imagine that such a system would crash. Like many, when the crash did come, he believed the economy would simply right itself and "bounce back."
Hoover's problem, in my opinion, was being formed in the mindset of an earlier time period. He was very conventional and couldn't encompass a crisis of the magnitude of complete economic collapse. The country needed a visionary leader at that interval, such as Franklin Delano Roosevelt, and instead had an everyday president who thought he was going to oversee peace and prosperity. Hoover could never overcome his deeply ingrained beliefs that government should stay small, not intervene in the economy, that charity should be private, and that the business world, even in an extraordinary crisis when its normal mechanisms weren't working, could fix its own problems.