Notifications on both

No - by design, your phone stops going off when you have the watch on, and notifications are directed to your wrist.

 

I just did a test. I received an alert on the watch but didn't respond to it then I checked my phone. The alert was on my phone. I then responded to my watch and the alert disappeared from the lock screen of the phone. I don't have sound on so I didn't test that part.

 

I remember buying the very first model Apple watch and that was my very first question was why my phone stopped making notification sounds.