This is incorrect. Armor takes a large amount of damage dealt to the player, but not all. If you are at 1 HP, and 100 armor, you can still die to a single bullet, even though armor won't be at zero. Fall and drown damage is also not affected by armor. Hence armor is not life.

Source: https://github.com/ValveSoftware/halflife/blob/master/dlls/player.cpp