As far as I can tell, there is no answer to this question. Access databases (usually .mdb files) are standalone, not connected to a SQL Server (or other) server-based database.
This is not correct. Connections to other databases can be created inside Access. I read and started typing too quickly, presuming server-driven situation.
It is possible that data can be extracted or exported from a server-based database and stored as an Access database. It is possible to import an Access database into a server-based database. It is even possible for MS SQL Server to read from and write to an Access database file through Remote Stored Procedures or "Link Tables".
But there is no required server connection in an Access database, and unless coded specifically, nothing in the Access database to identify a particular server to which it is or has been connected.
--> This is not completely correct .. an ODBC or other connection object inside the Access database should have information about the other end of the connection. I don't believe that info can be seen other than through the Access environment or a program, however.
The question was specific .. can the .mdb file be parsed with a command-line or text search tool to find database connections. While my answer did not really consider the "front-end" database scenario, I think is still stands .. I don't think you can interrogate the database in the manner described in the question. You can probably write a program to interrogate the Access database and get connection properties. But that wasn't what was asked.