A:Answer As far as I know of the answer is yes. Battery technology has improved greatly in the last decade. You usually no longer damage the battery by leaving it plugged in all the time, the battery charger usually detects a full charge on the battery and either turns off, or goes to trickle charge. None of my other items that use batteries have a problem with being plugged in all the time and work fine after being unplugged.
Bose is a company that consistently builds high quality products so I'm sure it would be fine. (And no, I don't work for Bose).