Using the small "r" republican reference here, just to be clear. Republicanism of the time, along the lines of Jefferson and his belief we should form a nation of small farmers with the right to vote mostly came to pass during his lifetime. During the Revolutionary period, this vision seemed the ultimate justice compared to British injustice. Every man with land, every man with a vote and representation.
While there were certainly other motivations and reasons for getting involved in the Revolutionary movement of the time, it is fair to say that republican ideology played a central role.
Republican ideology contributed the type of government that resulted from the American Revolution. Edward Countryman says in The American Revolution, that the one thing sure about the outcome of the American Revolution, if the rebels won the war, was that the new government would be a republic, not a monarchy; everything else was up for debate.
I assume that you are asking about the US Revolution...
The main contribution of this ideology was to make more people interested in joining the rebellion. This was most clearly seen in the impact that Thomas Paine's "Common Sense" had on the rebellion.
The rebellion was originally based not on republican ideals but on a fight for control of the existing government (fight between colonial and British elites). But the colonial elites needed more support from the masses. Republican ideology helped them to get this support.
So you can argue that republican ideology allowed the revolutionary movement to succeed.