Arguably No. At least according to Walter Berns. Or Thomas West's understanding of Walter Berns. Berns does argue that Rousseau did have more of a profound effect on America's Founding that most people are aware (indeed, Rousseau's notion of the "civil religion" is almost identical to the generic theism that Washington, Adams, Jefferson, Madison, Franklin et al. posited when they connected religious and political principles).
Here Thomas West notes what Rousseau's social contract teaches when war breaks out [quoting Rousseau]:
The citizens march readily to combat; . . . they do their duty, but without passion for victory. They know how to die rather than to win. . . . Christianity preaches nothing but servitude and dependence. Its spirit is so favorable to tyranny that tyranny always profits from it. True Christians are made to be slaves" (Masters trans. 129-30).
Then West notes Walter Berns' take on the matter:
Rousseau's nasty remarks are supported, surprisingly, by respectable conservative scholars such as Walter Berns, who maintains, "The very idea of natural rights is incompatible with Christian doctrine." According to Berns, if you don't put your neighbor's good ahead of your own, you are a bad Christian. But the natural rights doctrine of the founding says that you may put your own preservation first if it conflicts with another's.
If Berns and other scholars like him are correct, you cannot be a good Christian and a good American. George Washington's 1789 letter to the Quakers tactfully but firmly criticizes their refusal to serve in the armed forces. Good citizenship, Washington implies, requires that you be willing to kill the enemies of your country.
As I noted in my last post, Berns goes farther than I do in asserting the incompatibility between Americanism and Christianity. I would simply note that Americanism and Christianity are not the same thing; Christianity is compatible with American style republican government because Christianity is compatible with almost any form of government, even and especially tyrannical government that is hostile to Christians (indeed, the very government in which Christianity was born!).
Berns, after Leo Strauss, correctly notes that whenever you read about the notion of "state of nature" and contracts and rights, be it Hobbes', Locke's or Rousseau's version of the concept, you are reading an account of the origin of man that is "wholly alien to the Bible."