I can now say from personal experience that it IS possible to install the front mud flaps without removing the wheels, but not the rear.
On the front you will have to turn the wheel to full lock (easiest to hold there if you have an assistant or a strap of some sort) then you will have just enough room to drill the wheel well liner.
There is no way around the rear since you can not turn the wheels. You will have to remove them to drill the liner.