If it is already open (by any other session) in Exclusive mode, you can't open it again. It has to be opened in non-Exclusive mode.
If it is already open in non-Exclusive mode, you should be able to open it. If you can't, you should get an error message and code unless you have disabled warnings in your VBA code.
If your WORD session already has the database open, I think there should be a DBEngine, Workspace collection, and Databases collection that you could read. If so, the Database object representing that open database should include a name that is the fully qualified file string for the database. I could be wrong on that because I so rarely use VBA anywhere other than from Access. But I'm also pretty sure that if YOU have the DB open, there should be no barrier to you opening it a second time (again, as long as the FIRST time you opened it wasn't EXCLUSIVE mode.)