Not exactly. Keep in mind that the Westminster system was still relatively in its infancy. The first Prime Minister denied that he was a Prime Minister (this is fairly common a theme. Lord Landsdown in 1829 said "nothing could be more mischievous or unconstitutional than to recognise by act of parliament the existence of such an office."). At the time of the American Revolution, the King was heavily involved in governing and selected a Prime Minister in Lord North who was very much in agreement that there was no such thing as the Prime Minister. The entire cabinet was appointed by the King (who needed the consent of Parliament to function, but did not necessarily need to be chosen by Parliament). Given all that, the system had at least some resemblance to having two separate branches: The Executive (through the monarch) and the Legislative (Parliament), but the exact divide of power was completely ambiguous.

On top of that, there seemed to be a somewhat corrupting intermingling. The government was run by the King's ministers (i.e., the Cabinet). These were individuals appointed by the King. However, they were appointed from members of Parliament. It was not uncommon for the King to secure legislation he wanted by offering a minister position to an influential member of Parliament. Many at the Constitutional Convention abhorred what seemed to be essentially bribery. They responded to this by creating a strict separation of executive and legislative. Parliament to this day has members of Parliament govern through their cabinet position. The US Constitution, however, flat our prohibits any member of the legislature from becoming a cabinet secretary. If they get that position, they have to resign from Congress. The best Congressmen have are the ability to form committees that can supervise executive departments and recommend legislation. They lack the ability to act that ministers in the Westminster system have.

I'll also add that, while the King was the major villain in propaganda, Parliament was as big a problem to the colonies. All the hated legislation was passed by them, not the King. While I've argued that many of the elements that existed at the time were either adopted or modified rather than rejected, the framers of the Constitution had as much of a problem with Parliamentary supremacy as they did with the Monarchy. A separation of powers with an executive who could actually exercise his powers (for example, at that point no monarch had withheld royal assent to legislation for eighty years. Presidents have used their veto power from the beginning). The idea of separation of powers is an important distinction from the beginning designed to avoid any one group from becoming too powerful and is probably the biggest difference (although things were blurry over in Great Britain at the time, imo).

TL;DR: The Westminster system as we know it today was not clearly defined at the time the Constitution was created. Because of that, the Constitutional Convention could arguably be seen as taking the government that existed at the time and "fixing it" by changing the aspects that they viewed as most problematic.

My sources are wikipedia and things I've learned but can't properly source at this time. I hope a historian can come in and correct any errors I've made and supplement anything I've left out.