No. For whatever reason none of the other devices are synced with the website wishlist.
Each of the other devices (except Nook 1st Edition) has its own separate "on device" wish list not connected to the web page wish list.
For the Nook HD & HD+, you recreate your wish list via shop. Select a book, then tap on the white heart icon on the same page as "buy" and "free sample" button to add it to your wish list. To bring up your wish list, tap on the dark heart icon on the bottom left section when in shop.