well, they can't unbind, but they can AND HAVE removed items and sent new unbound versions in the mail to said character. I KNOW that can happen.
I will have to try that, since I have two items from a crime lord bag that bound when I crtl-left clicked them to see what they looked like and decide who to send them to.
edit- this happened with no popup warning saying they were now bound or would bind. the countdown timer just disappeared.