As in an absolutely radical period that took revolutionary ideals to their logical extreme.
I believe not. The American and French revolution were just too different in pretty much every aspect.
The French revolution happened predominantly in the cities, most notably in Paris.
It was an uprising by the disenfranchised lower classes against an all-ruling elite, notably the King. The elite held pretty much all the strings so their removal automatically meant a power vacuum. The revolution was decided by uprisings rather then battles and there was no real army so whoever controlled the revolutionary guards controlled the power.
The American revolution was predominately fought by organized troops in the countryside. It was a clear-cut affair between local separatists and rulers from overseas. The 'middle management' of town officials mostly sided with the rebels -and if they were not, there were accepted ways to replace them with at least a likeness of legality- so there was never any power vacuum.
This goes to say that there could have been some instances of Jacobin-like purges in some of the bigger cities like Boston or Charleston. There, like in France, a group of radicals could control the local militia to institute a reign of terror -neighbor against neighbor style. However with an organized army in the field, their power would only last as long as it took for a commander like Washington to lead his troops into town and restore order.