Will the BNAP automatically reset after I complete Day 365?

No, the app is designed to prevent you loosing your progress if you have not completed over 255 days of devotions. Provided you are on version 8.4.0 of the app or later, the app will ask if you would like to restart the year once you have read more than 255 days of devotions, including December 31st.

If you would like to restart from Day 1 before completing the previous year, you will need to either scroll to the top of the list view and tap on the 'Start a new year' button or reset the app (tap on Menu > Settings > Reset app), which will allow you to go through the onboarding process again and select 'Day 1' as your start point.