Hi
Yes that's what I've done in the past, but this time I updated my three machines as follows.
On my 'main' device, tried the obvious route, ie Sign In to Account, then go to Enter Product Key on the Help Center part of Norton 360.
After entering the Key, I get an error message - "Before you can start using your Norton subscription with this new key, we'll need some
additional information to register it. Please enroll at norton.com/setup. (-2027)".
So I follow the link and arrive at my account subscription details with only the option to renew at the Norton price (no sign of an option to continue just using the key I'd purchased separately).
So, I logged out completely and went directly to norton.com/setup. Signed in and from the two available options (Download and Enter a Product Key) I selected the latter.
Entered the Product Key, Payment Details page appeared with my Paypal info correctly displayed. Ticked the Agreement info and clicked OK.
Display showed Downloading, followed by Validating, and finally Installing. This all took less than a minute.
A final message confirmed Norton successfully installed and activated.
For my other devices, still on the 'main' system, opened Norton 360 and clicked on Install on Another Device.
In the Protect Another Device window, clicked on Copy Link. Clicked the Copy button and retrieved the generated link from the Clipboard. Sent this link to the other devices.
On the other devices, pasted the link into a browser and followed the instructions to download and install - again less than a minute's work.
So, a bit of a faff. Maybe a bit easier than entering the key at each device, esp if you don't want to send the key to somebody else.
Can't understand for the life of me why you don't seem to be able to enter the new product key at 'account level' and do the whole thing in one place. Maybe the original link from the error message wasn't working properly. Or maybe Norton just want to you give in and sign up at their renewal price?
Sorry about the long post. Hope it helps somebody else.