We just upgraded to the Business version and I'm kind of surprised that this feature or something like it is not a part of the software. It makes sense for a multiple user system to have the option to automatically lock a file when they open it, and it automatically unlocks once they save and close. The locking feature as is is fine, but people will never remember to unlock the file when they're done, especially if you're in and out of many files throughout the day.
A lesser but viable alternative would be to have the Dropbox badge for all file types, not just Office.