It looks like you want to connect data stored in either MS Access DB or Excel sheet with MS Access DB Engine. Yes, with 64-bit AutoCAD, the MS Access DB Engine must be 64 bit, which is a free download from MS.
As you stated, the computers of yours all have 32-bit MS Office installed. Thus, installing 64bit MS Access DB Engine could be an issue, or not possible, if the 32-bit MS Office suite is older version (2007, maybe even 2010, I could not recall exactly). But with later version of MS Office suite, at least MS Office 2013 or later, you can install 64-MS Access DB Engine with MS office 32bit in the same computer. With this said, making your CAD app dependent on MS Access DB Engine is not a very good choice. I'd avoid to use MS Access DBfor data storage whenever possible.
If you do go with MS Access DB engine, you do not need to create DSN (data source name) in each computer, as the other reply suggested. With ADO.NET, you can create DSN-less OldDb.net connection easily to read data fromo MS Access DB or from Excel sheet.
I know many people tend to use Excel sheet for data storage. In this case, you can use OpenXML to read/wriet data back and forth to Excel sheet (so that you can avoid the dependency to MS Access DB Engine).