Dynamic shapes based on mouse movement

Is it possible to track mouse movement (while a mouse button is down), record the mouse positions, and then programmatically create a 2D object that has the same shape that the user traced out with the mouse? That is, if the user drags the mouse in a square pattern, the code creates a square object; if they drag the mouse in a circular fashion a circle would be created. It would be best to be able to make any irregular polygon shape.

I know that Unity 2D doesn't like to draw lines, and I don't think line drawing on the GUI would be helpful since I need the resulting objects to interact with sprites in the game; but I'm hoping that there is some way to create irregular polygon objects in code so that I can just capture mouse movements and convert them into polygon vertices of dynamically created objects.

Is any of this possible with Unity 2D tools?