That’s the account with which I’m familiar.
I believe this battle is also considered that turning point that led to victory in the war.
Well, victory in the south certainly. Which then allowed the remaining southern US forces to reinforce Washington around Cornwallis at Yorktown, and prevented the southern English forces from attacking Washington’s trenches and reinforcing Cornwallis.
Cornwallis had come south from the NY-NJ-PA region to join up with the southern English troops.