(Assuming your points are 1 by 1 pixel)
You could create an invisible object called "CoorTest" for example.
You could then create a function with two parameter, x and y and call it "TestCoordinates" for example.
This function would set the coordinates of "CoorTest" to "FunctionParam(0)" (X) and "FunctionParam(1)" (Y).
It would then test whether "CoorTest" overlaps with any point, if yes, the fuctions return value gets set to 1, if not, to 0.
Like that, you could run the function each time you want to check for a coordinate already being occupied and getting the result as a return value.