The short answer, IMO, is yes, neocons have had the influence suggested by Parry and many others. That influence was up-front and obvious during the G. Bush administration but the groundwork that set the stage for that influence being a driving force had been laid out for years before. The very fact that for many years the neocons had been the major exponents of an attack on Iraq, which did become US policy, is at least prima facia evidence for their vital role in bringing about that war. It didn't stop there. Several more on their list of target countries have been attacked and their big prize, Iran, is still being pushed as an implacable deady enemy which can only be dealt with in one way.

 When the neocons influence came to the fore there were many who would not be called neocons who had similar ideas, even if somewhat different different motives and coming from other places, so they supported the neocon agenda.  Their own ‘American nationalist’ strategic vision largely coincided with that neoconservative agenda and, in essence, they shared basic assumptions. Cheney might be the best example of that. Therefore, I would not suggest that getting rid of all influential neocons would get rid of all the faults they have induced, but doing so would be a good start.
 Following is a list of some of the more recognizable names of neocons. I expect that most anyone who has paid even passing interest in our country's foreign policy adventures will be recognize that these persons have had a great deal of influence but would be hard put to demonstrate any benefit of their influence.
 Perle Wolfowitze, Feith Ledeen Libby, Krauthhammer, Frum,  Kagan Wurmser, Norman and John Podhoretz, Abrams, Frederick and Donald Kagan, Dershowitz, Pipes, Cohen, Bill and Irving Kristol. Max Boot, Schlesinger, and in what might have been the beginning, Levy Strauss.
  Here is a link to a "History Commons" piece titled "Neoconservative Think Tank Influence on US Policies" which which gives many ,many examples with supporting links.

http://www.historycommons.org/timeline.jsp?timeline=neoconinfluence&neoc...