Sorta!!! I've talked before about how if you really wanted to share an accomplishment on the Wii U, it was as simple as screen-shotting whatever you did and posting it to Miiverse. Which you can indeed do! But now that the Wii U is actually in our filthy little hands, a new feature has shown itself: tags. Look at that right there. Only New Super Mario Bros U and Nintendo Land use it so far, being the only titles that actually feature full Miiverse integration.
So we know the Wii U will feature a global achievement system called "accomplishments" when it launches in scant days. Oh, wait, we don't know that at all. This is one of the remaining Wii U mysteries—maybe there is a system there, or maybe there isn't. There have been hints, but there have also been plenty of things to suggest that maybe there is no such thing whatsoever, or that if there is, it's game-specific and not shared.