Can history provide us with any guidance as to whether the Anglo-Saxon powers occupying Iraq will be successful in creating a functional democracy?
Certainly, the British Empire had a pretty high failure rate in this regard. About half the countries that were once British colonies are now functioning democracies - but this does not compare with the failure rate of other empires. The only territories outside Europe that were ever occupied by the French which are now democracies were lost to the Anglo-Saxon powers two centures ago - Quebec and India to the British and Louisiana to the Americans.
Until the 1980s there was only one functioning democracy outside Europe that was not a former British colony - Japan. And Japan had been occupied and reconstructed by Britain's most successful former colony, the USA. A few others have joined the club since then, starting with South Korea and Chile, and now including a few other Asian and Latin American countries. All have become democracies under direct pressure of the United States.
The UN has no record of promoting democracy. If other European powers ever tried, they failed abysmally. The record of the Anglo-Saxon powers may be patchy, but it far exceeds everyone else.
And, of course, the two most spectacular successes, Germany and Japan, were both Anglo-Saxon projects.