Will iOS region monitoring call didEnterRegion on my app if my app is in a terminated state?

Yes, see Region Monitoring

In iOS, regions associated with your app are tracked at all times, including when your app is not running. If a region boundary is crossed while an app is not running, that app is relaunched into the background to handle the event. Similarly, if the app is suspended when the event occurs, it is woken up and given a short amount of time (around 10 seconds) to handle the event.

I have been searching for similar answer, but came across this: Region monitoring in ios 7

Seems like if the app is manually terminated by the user in iOS 7, location notifications will not wake the app to process it. Apple employee has commented here https://devforums.apple.com/thread/209302?tstart=0