We actually have some changes for how the Collector's Edition Angelic Wings function coming up! Currently slated for Patch 2.0.1, once a player turns on their wings, the wings will stay on even if the player logs out and logs back in at a later date.
To turn the wings off, you will simply be able to click the item to “use” the item again. This also means that you will be able to turn the wings on, and store the item in your stash, all the while maintaining the sweet visual effect on your character.
If a player sells their Angelic Wings item, however, then the buff will automatically be removed when you sell the item. You can of course get the wings back by creating a new character on the account in the same way that it works now.
Originally spotted on DiabloFans.