"Democratically elected leader" is always an interesting way to describe Mossadegh, the guy who cancelled the elections halfway through to prevent opposition gains, who allowed wealthy elites to dominate those elections, who banned the Communists from gaining a single seat despite being #2 in total votes, and who annulled the results that saw a KDPI member elected. It wouldn't be a longshot to say a good number of Iranian people were disaffected by their government even before the U.S. coup'd the government.

The elections were incredibly corrupt. Khomenei published his first pro-theocratic work in 1942, though the Shah's regime was almost certainly one of the main reasons he became marja in 1962. I don't think Mossadegh's policies would have been complimentary to Khomenei's line of thinking anyways, or that if the elections hadn't been overturned that radical Islamism wouldn't have taken hold. The Islamic Brotherhood had been active in the middle east advocating for theocratic government in opposition to the cultural decline caused by rampant Westernization for decades before the Iranian revolution.