I just want to add ... you asked ...
>> Is the MSWord doc simply querying the MDB file directly on the fileshare using the Jet engine on the fileshare. <<
And Bannana has explained that JET is a Database Engine that is INDEPENDANT of Microsoft Access. JET was actually part the MDAC for some time, so you got JET with Windows XP. But it is important to note that when you are asking and receiving data the JET engine is working on the machine that is doing the asking and receiving, the server that stores the data does absolutely no work toward the data request what so ever. Server B is merely a disk holding a file.
Also ... in "proper" terminology, the correct way to say this:
>> Server B has a copy of an Access DB at the mapped drive location <<
Would be ...
Server B has a JET formated database file that can be accessed through a mapped drive letter.
The KEY is that it is not
really an Access database (although an .MDB is even refereced as an Access Database in MS documentation!!), its a JET formated database .... Access merely utilizes the JET format to store its objects and data (by default at least).
Also of interest may be the information that Access does NOT interface DIRECTLY with the JET database engine. Under the hood, as well as, in VBA Access uses an API (Application Programming Interface). Access really really really likes to use DAO (Data Access Objects). DAO is the object model that Access Objects (forms, reports, queries, and tables) use when manipulating data (even in A2000 where ADO was the default object model for VBA!!). Also, Access can use ADO (ActiveX Data Objects) form and reports when forced to

. In VBA both object models can be utilized extensively to interact with the JET database engine. Note that when data is manipulated VIA ADO or DAO objects in VBA, the Access environment is merely providing the enviroment for the code and is not doing anything with respect to data requesting or receiving! ... interesting eh?....
So the path for accessing data stored in a JET formated datafile is ...
An Application (ie: VBA, Word, Excel, Access) works with an API (DAO/ADO); the API works with a "Data Provider" (OLE DB, DAO); the data provider communicates with the DB engine; the DB engine fulfills the request and returns the result to the data provider, then the data goes back up the path. I know there are many books the lay out this topography ... I know that chapter 17 (the first of the four chapters regarding ADO and DAO that I wrote for
this book) details some of this out for the reader.
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Here are some articles that may be of interest (I will post more if I can find some ... I found a bunch while writing those chapters!):
http://blogs.msdn.com/data/archive/2006/12/05/data-access-api-of-the-day-part-i.aspx
http://msdn.microsoft.com/en-us/library/ms722791.aspx
http://support.microsoft.com/kb/275561
....
EDITS ADDED >>>
WOW! .... lots of conversation during the composition of my post! ... Hopefully the info is still helpful.