The Tennets (primarily Gilbert Tennent) were involved in the Presbyterian contribution to the Great Awakening.  The Presbyterians broke into two camps — Old Sides and New Sides which paralleled the Old Lights and New Lights of the Congregational churches.  The Baptists don't really get involved until just before the Revolution and their splits occur during the Second Great Awakening as fallout from the Abolition Movement and the rise of the Campbellites (aka Disciples of Christ).

I had heard that the Presbyterians (I believe from Scotland) were more of the "upper" echelon of social status.  Wouldn't they have sided more with the status quo "institutionalized" belief of the Church of England?

Many did, but they suffered schism too because of the New Birth teachings.