Do whatever works best for you.
No one here cares how many times your Mac chimes at you with a new notification. Whether or not it's "correct" [sic] is up to you.
Personally I don't use Google Chrome. It's a well known resource pig and an repeatedly identified privacy violator. Note that I accept Google's fiscal success as an indirect shareholder (most Americans with retirement accounts or pension funds are).
I still use a few of their services (Google Voice, Google Translate, YouTube) but neither Search nor Mail.
Note that app notifications themselves are neither positive nor negative. They exist for many apps.
Incoming phone calls are technically an app notification. Do you want your phone to notify you or not (sound, vibrate) when there's an incoming call?