Answer: In my experience, figs are not easily grown in your winter hardiness zone (based on your zip code you are gardening in zone 6) due to the severity of the winters and the relatively short growing season.
Whether or not a newly planted fig could successfully bear a late season crop the first year depends on its overall condition, the planting site, the care it receives, and the weather that year. Even if you purchased a plant with immature fruit on it, the fruit could drop if the plant becomes stressed, and transplanting is by nature a stressful event for a plant. And, it is better to transplant these while dormant in early spring, so it is already a bit late in the season for planting. And even if the fruit held, it might be too cold too early in the fall for it to fully ripen. So I would not be comfortable promising a crop this year -- or any year -- for all those reasons.
Brown Turkey has relatively good winter hardiness and you may have success with it over the years if you are willing to experiment and see how it grows for you in your garden. It would typically freeze back to the ground and then regrow from the roots each summer, potentially bearing a late crop. (When it freezes back like that there is no chance for an early breba crop.)
I'm sorry to sound so discouraging. There are gardeners who do manage to grow figs successfully in zone 6. Here is additional information about how to grow figs in a colder winter climate such as yours. Your local professional nursery staff should be able to help you evaluate whether you have a particularly favorable spot for this plant, or not. New plants benefit from extra winter protection the first few years while they are becoming rooted and established as described in the article. It may be helpful to you in deciding whether or not you want to give it a try. You may need to cut and paste the complete url into your browser in order to make it work correctly.
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