Yes. This ensures functionality in all of the Google apps(Gmail, Youtube, Play Store) and also offers a easy way of backing up contacts and data and provides for a easy transition between Android devices. So if for example you buy a new Android phone the only requirement for you to transfer all of your contacts and apps is to just log in on the new phone with your Google account.
Important: Please try to make your login details as memorable as possible as to not get locked out of your account and potentially lose data if you don’t have a secondary way to reset your account.