Really doesn't seem that way when I tested it. Peasant archers vs. pikemen in all 3 armor levels, 5 volleys repeated 10 times for each level. Effect was negligible. Pikemen in steel breastplates dropped almost as fast as those in their t-shirts, an average of 30 losses vs 32 for unarmored after 5 volleys. Armored pikemen (stuff that comes with armor) took very few casualties in comparison, around 18. Adding 3 to the base armor of pikemen (giving them 6 armor with all upgrades) made them just as resilient to arrow fire, 20 losses on average.
On the face of it, the upgrades seem to be the RTW +1 armor per level system. It doesn't seem likely that there is any "hardcoded" armor level system ingame. I wish someone with an official line would comment on this.