You can disable the notifications on your phone (at least on Android) but you cannot on the website. I found this Google Group post where a Google Community Manager actually replied with:
I can understand where you're coming from and will pass the feature
I usually ignore the notifications and sometimes appreciate the
reminder that a photo has uploaded when I may have forgotten about it.
But I hear you :)
That was in 8/11. So far the update hasn't been made to say that it's a notification you can turn off. I also ran through settings on the browser and it's definitely not implemented yet.