Yes. Background sync keeps your games and achievements up to date without you having to open the app. It is switched on during onboarding unless you turn it off there. Later you’ll find it under Settings > Sync (open Settings with the gear icon at the top right of the Profile tab). There you can switch it on or off and choose how often it runs: every 3, 6 or 12 hours, daily, or weekly. The default is daily.
The sync only runs over Wi-Fi and not between 11 pm and 7 am. The operating system decides exactly when it starts, so the interval you pick is a minimum gap rather than a fixed time, and on iOS in particular a run may come later. If the system cuts a run short, the next one picks up where it stopped.
If you don’t want to wait, tap “Sync now” on the same page. With notifications for new achievements turned on, the app lets you know as soon as a sync finds something new.