Yes. There's no doubt that the English longbows were a force to themselves. They were lethal in piercing armour but they were still used in generally the same manner. To open up the battle by forcing the enemy to take a defensive stance and "thinning the herd" (so to speak) before your own infantry engages their forces.

Once the infantry engaged however, you didn't want to be raining down arrows on your own men and so the purpose of the archers largely changes to a completely different purpose; controlling the flow of battle with strategic use of volleys.

And yes...the Mongols changed everything with their horse archers. There's a reason a good part of the population is descended from Genghis Khan...

Armies relying on archers often had a continuous resupply running towards archers in position.

Yes indeed. Generation Kill is the only thing I've seen that got close to reality. I was in a unit that did exactly what was shown in that show, and for the most part they nailed it. They showed the confusion, stupid orders, lack of proper communication, the constant fatigue, and the crazy shit that just happens out of nowhere when you have a bunch of 18-20 year old testosterone rage machines running around with serious hardware.