App updates from a different country's iOS App Store?
Yes and no. Let me explain:


You will be able to update the app, but only by logging into the same U.S. Apple ID you used to download the app. You cannot download updates any other way.
Since the app in question is not available in the Turkish App Store, you're also not going to get notified via the App Store of any available updates (i.e. unless you are logged in with the U.S. Apple ID you used to download the app).
However, depending on the app itself, you may get a notification from the developer via the app when an update is available, in which case you know to log in with the U.S. Apple ID you used to download the app in order to install the update.
In the event that the app becomes available in the Turkish App Store at a later date, you will actually start to get notifications via the App Store app when updates are available. However, you would still need to log into the U.S. Apple ID you used to download the app in order to install the update. (NOTE: If this were to happen, you could then delete the app entirely and then redownload it using your Turkish Apple ID in order to manage future updates without the need of the U.S. Apple ID.)