Yes, JMP can connect to a database through the ODBC driver for that software. See Help > Books > Using JMP > Chapter 3: Importing Data.
So, with 64-bit JMP 13.2.1, when I click on File -> Database -> Query Builder -> New Connection -> Machine Data Source -> MS Access Database -> OK, I get the following error:
"[Microsoft][ODBC Driver Manager] The specified DSN contains an architecture mismatch between the Driver and Application"
I am glad that you resolved the problem. It is exactly the problem that PM suggested. It is documented here, found by searching on "specified DSN contains an architecture mismatch" at the Support section of the JMP.com site.