I don't really understand this "synching" thing very well. If I get the new tablet, will my progress in the games on the NC transfer to the new device? Do I just register it and then any Apps I have purchased should work on both tablest at the same time?
If you register both of the devices to the same B&N account, than any app that has Nook HD listed as a supported device should allow you to just go to your library, go to your apps, and download those apps.
Its a lot like if you buy a Nook book, you can download it to a Nook Color, or a Nook Tablet, or a Nook PC app, or a Nook app on an Android phone.
That is not really syncing, it is downloading the app from your archive. Its just like if you archive an app, the local copy is deleted from your Nook Color, but your account still records that you have the right to download it again. If you also had a Nook Tablet, and it was a Nook Color / Tablet app, you could download it into your Tablet from your archive.
How they will handle new HD versions when you already own the SD version ... that I don't have any idea. It might depend on the specific publisher.
There is also a different kind of "sync", which is syncing your place in a book between two different devices. I doubt that Nook will support that for games, though maybe they will support that for movies downloaded/streamed from the Nook Video store.
Each device the game is downloaded to receives a unique copy. The results are not synced with copies on other devices. Probably a good thing, that way multiple device households can buy once and each player has their own history. My Google Play games work this way also. Partly this is because the devices sometimes have different versions or versions are not available for some devices.