This actually calls back to an answer I originally made when the episode aired, featuring the event you describe.

Not to mention the Bolton archers firing indiscriminately into the backs of their own men. Yes, it could and did happen but never with the intention of building a corpse wall. It was extremely unwise to shoot the backs of your own knights and cavalry because they were the elite of society and your best soldiers. Not to mention it could invite your cavalry attacking your own archers. At the battle of Crecy, the French knights charged down their own crossbowmen (for a lesser offense of cowardice and simply being in the way). Doing this also invites a dagger to your back next time you're alone with a few of the knights who lost kin to your archer's arrows.

Furthermore, the biggest utility for archers was to harass, slow down, and disrupt the enemy; by forcing them to hide behind shields, get wounded and retire, or get outright killed. Most people that suddenly find an arrow in them are not going to be effective in combat. Once the melee begins, this utility is greatly diminished as the movement has stopped, the front lines are engaged, and there is risk of hitting friendlies. Unless there are other groups of enemies not yet engaged or on flanks, the archers would have to re-position themselves; which may put them at risk of being caught by enemy cavalry.

Short answer is: Yes, but only if there were enemies nearby not yet engaged (such as a reserve or flanking force). Highly unlikely, if the enemies were engaged - the risk of hitting friendlies was too high.