Regular season overtime rule clarification

The current NFL rule:

• No more than one 10-minute period will follow a three-minute intermission. Each team must possess, or have the opportunity to possess, the ball. The exception: if the team that gets the ball first scores a touchdown on the opening possession.

My question:

In the unlikely event that the initial receiving team in overtime uses the entire 10 minute overtime period, kicking a field goal with no time remaining, would the opposing team still be granted an opportunity to possess the ball as defined in the NFL rule?