They would have been aware of the difference between Continental legal systems based on Roman/Imperial models and the English common law. Their familiarity with Blackstone would aid in that, since his introduction is one of the more famous discussions of the distinction in legal history.
You must remember, as anyone must, who would pursue that valid line of analysis, that the Founders were SPLITTING from monarchy. Blackstone was a committed Monarchist. While the Founders took the English and Scottish common law heritage for granted in large part, that large part being relations between citizens, in the part of establishing the rules of government and the requirements for those in positions of authority within that government they had to draw wisdom from other wells.