The short answer is that the typical voter in the US in the late 18th century was well aware of both the work of American and non-American enlightenment thinkers.

In the late 18th century, a "typical voter" would be, in most states, a white, land-owning male. Charters of Freedom - The New World At Hand (an archives.gov online exhibit) has this to say:

At the time of the first Presidential election in 1789, only 6 percent of the population–white, male property owners–was eligible to vote. The Fifteenth Amendment extended the right to vote to former male slaves in 1870; American Indians gained the vote under a law passed by Congress in 1924; and women gained the vote with the ratification of the Nineteenth Amendment in 1920.

As Harvey Graff writes in Legacies of Literacy,

In the "new world," the level and social distribution of literacy were not static during the eighteenth century. Regional differences, as well as social divisions, had not been erased. New England again led the way. The male literacy level there rose slowly to 70 percent by 1710, and by 1760 it had leapt to 85 percent. Even comparatively impressive literacy levels and a cultural impetus toward schooling, the data suggests that many New Englanders in the eighteenth century still were "closer than we have imagined to the credulous word-of-mouth world of the peasant, closer to its dependency on tradition and on the informed few"

Graff argues (and his arguments are echoed by Lawrence Cremin in American Education: The National Experience, 1783-1876, among other sources if you're interested) that the gulf between "the informed few" and other moderately literate white men was roughly as great as the gulf between someone who is moderately literate and someone who is completely illiterate. That is, the upper echelon of literate folks were not just literate, but highly literate, i.e. widely read. While this would change as the 18th century turned over into the 19th century and more and more folks gained a greater degree of literacy, but remained relatively narrow in terms of their reading choices (think newspapers, the Bible, some spellers/primers, etc.), within the parameters of your question it suggests that there is fairly direct correspondence between "being a voter" and "being widely read."

Now, the real question is does "being widely read" mean "being widely read in the philosophies of the Enlightenment?" And to that I directly to Cremin who, considering Thomas Paine's intellectual heritage, writes this:

Paine could easily have imbibed Newton and Locke, Collins and Toland, Rousseau and Condorcet, without ever having read a word of them. Like others of his generation, he received Enlightenment affirmations from newspapers and magazines, from informal study groups and itinerant lecturers, from conversations in taverns and disputes in coffeehouses. **And, like others of his generation, he mulled them, argued them, and translated them into his own terms, producing a new and powerful version that was at the same time coarse and clear, simple and persuasive, audacious and reasonable.

What this indicates (something that Henry Mays' Enlightenment in America points out) is not only that the so-called "philosophies of the Enlightenment" circulated throughout America, but that America was an equally important site of Enlightenment-era philosophizing. Though he calls for a clearer demarcation between these American and non-American Englightenment-era thinkers, Mays writes,

Locke, Hume, Voltaire, Rousseau, and Jefferson can be described and admired together. These men shared certain very generous loyalties....The distinctions among them and their followers must be clearly made if one is to treat successfully the history of the Enlightenment: its spread, its victories, its defeats.

So, to return to your question, there is a problem with the formulation that the founders based the structure of the country on the work of other enlightenment philosophers. It is more accurate to say that both the founders, in their writings and their doings, participated in the same, very roughly drawn thought era as did other thinkers such as Locke, Rousseau, Hume, Newton, Condorcet, etc. And the residue, if you will, of this thought era (i.e. all the writings) circulated widely within and was influenced by a class of highly literate folks (mostly white guys), both in the US and abroad. And this class of highly literate folks was, for the most part, the "typical voter" in the late 18th century United States.