Yes, which is why bronze was expensive. Pre-iron equipment would have been primarily leather and stone, like the Cuirass made of hardened leather and studded with some metal. See: Lineothorax or something similar, which is incorrect because it would NOT be made of linen. Still, some well-made leather armor would provide a lot of protection. We're not talking about common work boots nowadays, but it had more the consistency of sheetrock, you could bang your knuckles against it and come back bruised. As war was, and is, an art form in itself, there were designers to work on how to use things like leather and rope to protect a soldier against swords and arrows. DF doesn't do much to simulate hardened leather, it's more like clothing leather.
This is all because copper was a common enough metal, but rather weak, and tin was rare but essential for bronze, and bronze was amazing for the time. Spears would probably be preferred, as they could be tipped with bronze but made of wood, while a sword would need a solid blade. A soldier's equipment would be a spear or club, maybe a sword for better infantry, and leather or packed cloth armor. War was brutal, people died, a lot. Full bronze plate armor was extremely expensive, and more for officers.
When metalworking allowed iron to be used for weapons and armor (formerly too brittle, a bit of carbon would help) allowed soldiers to get real armor and weapons made of cheap iron, instead of reserving expensive bronze for the officers. Of course, cheap iron armor was still far beyond a commoner's means. One did not simply 'become a warrior' but would probably grab a pitchfork and leather tunic and go die. War was still very brutal and only good or wealthy soldiers would get true equipment. A suit of Crusader armor is comparable in value to a modern house (before the housing market crashed).