I was a SCA Combat Archer back in the early '90's.
Were they effective?
Could be, especially if you were fighting back when bird blunts & chemical stoppers where used. They were good at either firing into mass formations or for taking out select targets. After they went to APD's & Baldar blunts they became a bit of a joke.
How did you fight combat archers?
Used to be all you had to do was get within 5 yards of 'em and call em dead. So if some archers were causing you pain just send out some plate armoured boys (plate being proof) and kill 'em. Now if you have a lot of 'em you just go after them with your shield or glaive and chase them down. At Antir/West War in '93 or '94 I was able to show that Antir archers couldn't hit a dancing man at 30 paces. I was that man.
Siege weapons, Javelin's, and good throwing axes can be much more efficient.
I can honestly say that CA has changed quite a bit in the past 20 years. Way more than Heavy or Rapier.
Do you have any other questions? I have more stories than that if you would like to hear them.