Yes and No. Microsoft Access 2010 (and higher) comes in 32 and 64 bit versions. Only one of these versions can be installed on a machine. Both versions create and use MDB and ACCDB databases that can be used with either version (and earlier versions of Access).
Total Access Admin 2013 can monitor databases created by the 64-bit versions of Microsoft Access 2010 and 2013. It can also monitor and log the users that connect and disconnect from it. So if the database is placed on a shared drive, Total Access Admin 2013 can monitor it whether users are using the 32 or 64 bit version.
To do so, Total Access Admin needs to be installed on a machine that has Microsoft Access 2007 or the 32 bit version of Access 2010 or 2013. It cannot run on a machine with just the 64-bit version of Access 2010 or 2013 installed on it. However, it can run on that machine if Access 2007 or the free runtime version of Access 2007 is installed on it.