Arabs watched the democratic process in all its glory take place in Iraq along with several relatively modern campaigns, the drafting and voting on a Constitution, and the rest of the trappings of how to put together a democratic system.
All under an amazingly inept American administration which botched the reconstruction and continually pushed its favourites? You will recall that Bremer fought democracy tooth and nail. That he unilaterally cancelled the results of municipal elections, and that he fought elections tooth and nail until the Ayatollah Sistani gave him no choice.
Unfortunately for your thesis, to the extent that the Arab Spring had any inspiration in Iraq, it was inspired by anti-american movements. Realistically though, its pretty clear that the Arab spring movement was indigenous to the countries that it occurred in.
Your notion that the 'example' of 'functioning' democracy in Iraq had any influence on the evolution of the Arab Spring movements is ignorant and condescending at best.
You do realize that just about all of the Arab states have something of a joint shared history with European democracies. That through cultural exchange, economic ties, and history, the populations of most of these Arab states had an understanding of democracies. You realize that even several of the monarchies had representative houses, that Algeria and Lebanon had had electoral traditions, and that even Egypt despite being a dictatorship/oligarchy still maintained democratic trappings.
For your poetic thesis to have any credibility, the Islamic world would have to have existed in a complete vaccuum, one which precluded any history, and one which carefully ignored or excluded the American occupation from notice.
Sorry, but your argument does not deserve to be taken seriously. It is merely a self-serving effort to rationalize an imaginary positive outcome from the Iraq War and occupation. The fact that you've gone to such desperate and abstract lengths speaks volumes about the war and occupation.