Maybe, but most modern mechanical fans are designed to go flat by 4000 RPM. If they don't go flat they would eat even more HP.
We put on a deeper core support airdam and electric fan and the overheating completely disappeared, with no changes to the radiator, water pump, coolant or thermostat, and we actually can turn the motor faster now because it is only 190-200 degrees, now.
After the electric fans were added, we were also able to block off the upper grills for better aero, which completely eliminated front end lift at speed.