There is no way to definitively answer this question, which has been at the heart of historical debate about the Revolution for many years now, and historians by no means agree on its answer. Historians at the beginning of the twentieth century tended to view the Revolution as a profoundly conservative affair, focusing on the economic interests of elites and the efforts they made to contain any potentially radical reforms. According to Carl Becker, one the preeminent Revolutionary historians of the period, the Revolution was about two things, "home rule" and "who would rule at home." Later historians rejected this class-based analysis, but still noted what they saw as an ideological consensus among elites, who fought to preserve their rights, not to create any sort of new society. A later generation of social historians, beginning in the 1960s and 70s, point out the many ways in which the Revolution failed to live up to its rhetoric. The most famous recent book on the topic, The Radicalism of the American Revolution, by Gordon Wood, argues that the revolution, while limited in its goals, unintentionally unleashed radical democratic ideals, which took root despite the Founders' fears of democracy. Other historians have focused on the Revolution from the "bottom up," showing that it involved the actions of urban crowds, agrarian radials, women, Native Americans, and slaves, who played a role in pushing the events of the revolution along and altering them to fit their circumstances. Most historians would now allow that because of the changes it set in motion, albeit against the wishes of many elites, that the Revolution was, in its way, radical.
I would argue that the American Revolution did not start out to be radical, but that it ended up being quite radical indeed.
The leaders who started the rebellion against Britain were largely uninterested in what we would now think of as democracy. They wanted self-rule for the colonies, but they did not really think that the common people should be heavily involved in ruling themselves. Had the revolution continued as they hoped, it would have been quite conservative, with an American elite simply replacing the British elite at the top of a hierarchical society.
However, the common people can be said to have hijacked the rebellion. These people, fired by things like Thomas Paine's rhetoric, demanded the sort of equality spoken of in things like the Declaration of Independence. What came out of the revolution was a society that was much more egalitarian than it had been before. This was a truly radical change.