They are not bound. Simply do a search on the AH for "forge prize box".
http://wiki.spiralknights.com/Forge#The_Forge
"Forge Prize Box containing a random assortment of various rarities and other items (prize box and contents are bound)"
Yep, forge prize boxes aren't bound to you.
"Forge Prize Box containing a random assortment of various rarities and other items (prize box and contents are bound)"
Yep, forge prize boxes aren't bound to you.