I haven't seen the documentary but as a basic idea I would say the answer is no. "Radical Islam" is a difficult concept to define but I would make the case that it emerges long before "neo-conservatism" (which is likewise difficult to define.) Much of what I'm about to talk about is terminological and up for debate but I'll try to explain my terms where necessary.

Modern Radical Islam can be seen as an intersection point of two sets of understandings or beliefs within Islam. The first is often called "fundamentalism" which derives its name from the Christian movement of the same name. While Islamic fundamentalists trace their routes back to the time of the Prophet (7th century) for the modern movement the most important development was the ideology of Abd al Wahab, whose alliance with the Al Saud created the early Saudi State and forms the ideological basis for modern Saudi Arabia and the Wahabist movement. I would describe this as a longstanding trend within Islam, because in many ways it bears significant resemblance to the far earlier movements surrounding Ahmed ibn Hanbal, who lived in the 8th/9th century AD, and was concerned with a pure Islam concerned only with the issues on which explicit guidance exists from the Quran or the Hadith.

The second is the advent of "Islamism" which is a modern political movement that emerged at the end of the 19th century. Islamism was both a response to western imperialism in Islamic lands but also a positive answer to how Islam can exist in the modern political world. The most important early thinkers here would include Muhammad Abduh, al-Afghani, and I would particularly emphasize Hassan al Banna, who founded the Muslim Brotherhood.

The early Muslim Brotherhood had many of the features that are today associated with modern radical Islam. It was closely associated with charismatic leadership. Al Banna very much believed that the Brotherhood needed to have a military wing, which was referred to as "The Secret Apparatus." This wing, by the 1930s was engaged in street battles with Egypt's fascists, communists, and nationalists, all of whom were strongly influenced by what was going on in Europe with the brown shirts, black shirts, blue shirts, etc. By the late 1940's the Brotherhood was conducting a bombing campaign on Egyptian politicians, Egypt's Jewish community, and anyone else who opposed them.

I would argue that this is the start of "Radical Islam" in any meaningful definition, conducting terror attacks on civilian populations inspired by a political Islamist ideology. It's possible that the documentary discusses the appeal of Radical Islam as coinciding with the rise of neo-conservatism, but as an ideological outlook, the conclusion of the neo-conservatives that American conservatives should make peace with the welfare state while espousing a more hawkish foreign policy has anything to do with the emergence of the late 19th early 20th century ideologies of political Islam sounds unappealing to me.

edit: if you have a link to the documentary I'd be curious to watch it. It's possible they're making a very different kind of argument, which perhaps you could expand upon in a reply or a comment.