The answer is essentially yes, but with caveats. Democracy, by which in this case I mean the electorate voting a representative parliament, was and had been for a long time the practice in England. The earliest British settlers in the New World were not Puritans but adventurers looking for land, their fortunes and a new life away from the strictures of life in Britain. These people founded Roanoke and Jamestown, the Puritans came some 14 years later. The earliest settlers certainly were looking for freedom from the rigid social structure of Great Britain, and obviously believed in democracy as can be seen from their various documents. Of course, they were somewhat restricted in their status as de facto employees of the trading company which financed the settlement.
The Puritans had a more complex situation. Non-members of the Anglican Church were forbidden to hold office in Britain, but since the settlers of Massachusetts were not Anglican the Crown was allowing them to function in their colony as if that restriction did not exist. They certainly sought freedom for themselves in their new home, and established a democratic colonial government. They did, however, intend their particular colony for themselves and not other religious groups. They could not exclude Anglicans, but they did exclude Quakers as time went by. So the answer is yes, the earliest settlers believed in freedom and democracy, but perhaps not entirely in the way Americans view these terms today.
The previous post revealed some interesting aspects about the question. I think that an argument can be made about the statement holding some validity. American colonists expressed a political notion that articulated a passionate belief in the preservation of economic and political notions of freedom. Much of colonial political thought expressed a profound protest of infringements on their social and material expressions of freedom. Patrick Henry's speeches and Jefferson's writings, along with the Sons of Liberty, articulated a vision of liberty which espoused individual freedom. Certainly, one can suggest that the drafting of the Constitution was done so understanding the reality of political abuses. These violations of the public trust compelled them to adopt a government predicated on the notion of representative democracy and the belief that government should work towards fulfilling the needs of the many.
False. The early settlers weren't Americans. They were English puritans who left England intending to build a sepratist colony based on strict puritanical teachings. Queen Elizabeth the 1st of England decreed that everyone had to attend the Church of England. These puritans wanted their own church. They had no intention of creating anything democratic and would have been alarmed by the modern definition of freedom. They were fairly extreme protestants who wanted an isolated community away from anyone else where they could not play music, not enjoy themselves and worship God in a very strict and humorless fashion.