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we need our user's "bit-type" version of ACAD to match their "bit-type" version of Office...
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Are you saying that you need choose 32 or 64 bit AutoCAD for the user because of MS office he uses (32 or 64bit), just because of the need to access data in MS Access DB? That would be very bad and definitely "not be popular" as you expected, and very likely you do not have to.
Firstly, let's make it clear that MS Access is both data source and frontend user desktop app that could be in the same file (*.mdb/*.accdb). Ideally, if there is user interface, the UI app and data source should be separated as 2 files (*.mdb/*accdb). The *.mdb/*.accdb file as data source, can be accessed by either 32 or 64 bit application (MS Access fronend, or AutoCAD, in your case) via MS Access Database Engine, 32 or 64 bit respectively. Since in most cases MS Office suite of 32-bit os used, MS Access Database Engine 32-bit is usually installed with MS Office (whether MS Access is included or not). In older MS Office (2007), the computer can only have 32 MS Access database engine, or 64 bit one, but not both. With later office (2010, 2013), it is possible to have both (32 and 64 bit) MS Access database engine installed (but the installation might be tricky, expecially for MS Office 2010).
So, as long as you are not stuck with older MS Office (2007, since it was the first version of MS Acesss that dropped MS Jet Engine and used MS Access Database Engine), you are free to choose AutoCAD 64 bit, regardless MS Office being 32 or 64 bit. Most likely, you'd use AutoCAD 64-bit. Therefore the only thing you need to make sure what your plugin requires is to install 64-bit MS Access Database Engine, which is the prerequisite of AutoCAD (64-bit), not of your Plugin (so, you do not have to feel sorry if the data access does not work in your plugin due to missing 64-bit MS Access Database Engine).
With all said, using MS Access as data sourse isn't a good choice. If your user likes the UI available in existing MS Access, you can separate the data into other type of database (SQLite, SQL Server Express...) and stiil let user to use the same MS Access UI, and AutoCAD can access the data direcctly to the back end. Better yet, the backend data may be wrapped into a backend web service, so the 32/64 (or future "128 bit" :-)) issue can be gone forever.