The various okras I've grown over time seem to start producing in the neighborhood of 60 days from seeding, give or take a couple days. So if you planted tomorrow you should get your first pod around October 1st.
Keep in mind that for the first several weeks you'll get a pod from the central leader maybe every other day until the side branches develop to the point where they start kicking out pods too. That's the multiplier effect, when you start getting enough okra to actually do something with.
I don't know when you get your first hard frost but regardless, it would be an interesting experiment to plant a couple just to see what you get. After a rain you could loosen and amend just a few planting holes instead of having to till a bunch.
Go for it!
