The same account? Yeah. If you have a 3DS or a Wii U then buy the other console, you can log into your current Nintendo ID on the new console to have the same account on both.
If you currently have two different accounts on both, you can add your 3DS account to your Wii U as a second user.
If you have purchased games from the Wii U's eShop you will have to talk to Nintendo about putting all of your purchases on the same account, otherwise if you want to make your Wii U a single-account system you might lose your purchases.
The Nintendo ID works for most systems, from what I understand. I have never had an issue with it, at least, but then again I do not really rely on it for anything. That said, though, the more that you can sync them up and use them concurrently the more that you can really get out of them, so I would say utilize it as much as you can. Good luck and thanks for sharing.