You can have large army if you have lots of money.
Reliable source of lots of money are lots of BIG cities with lots of people working lots of road tiles.
Big cities will get big only if people are happy.
So yes, you use markets for both keeping people happy which results in more money for a bigger army.
For me getting a lot of luxuries helps and a market is a must. I'd rather build a market, than happy buildings or sliding the happy slider any further than 10%.
Not only that, but early on, if you have currency first, you can sell it off. The AI seems to love it. You can get easily $20-$40 per turn from most.
And playing off of currency, eventually banking you can make an even bigger killing selling to others.
And even further if you're first to get Economics?? not sure which one it is that lets you eventually build the "pay all upkeep for all commerce buildings" wonder.
You'll be swiming in cash since your market will have no upkeep.
Currency definately important to my style of play.