Yes.

I should stress that Greek city-states did not have a military in the modern sense. There would be little or no state-funded production of arms and armour, and no state arsenals with racks of helmets and spears like in Troy or Lord of the Rings (at least until the later 4th century BC). In times of war, every adult male citizen was liable for military service; if he was called up, he was expected bring whatever arms and armour he could afford. Many people would not be able to buy anything beyond a few javelins or a sling, and many others would have been armed with the shield and spear that had been passed down to them by their father or grandfather. Still, there was a significant and ongoing demand for weapons and armour whenever people were required to meet their military obligations.

In small communities, this demand would be met by the local smithy or by traders on the market. Bigger city-states might have large numbers of workshops or even entire neighbourhoods that could make, repair and sell weapons. When the Spartan king Agesilaos equipped his army at Ephesus in 395 BC (a very rare example of state-funded production of arms), he is said to have put the whole city to work:

He made the whole city in which he was quartered a sight to see. For the market was full of arms and horses of all sorts on sale, and the coppersmiths, carpenters, workers in iron, cobblers, and painters were all busy making weapons of war, so that you might have thought that the city was really a war factory.

-- Xenophon, Agesilaos, 1.26

In the largest communities, notably Athens, there were actual weapons factories (ergasteria). Several prominent figures from Athenian history owned sword factories or shield factories; the orator Demosthenes inherited a sword factory in which 32 slaves were permanently employed. Apparently, a male citizen population of about 25,000 provided a high enough demand to make such factories profitable. Part of the work would have come from the Athenian government equipping war orphans at state expense, but the rest would have been private purchase. The slaves working in such factories were highly skilled and therefore worth a lot of money. Their number suggests quite an advanced level of specialisation in the actual tasks of each one - though we probably shouldn't imagine assembly-line production. The weapons and armour we find are always unique and can vary quite radically in shape and size, partly because - as Xenophon notes elsewhere - it was very important to get armour and a shield that fit you, or else it would only be a hindrance.

As an aside, the picture you saw is probably the collection of Corinthian helmets found at Olympia (was it this?). These helmets were not mass-produced for a single campaign, but taken from countless battlefields and dedicated over a period of more than a century.