The Easysoft ODBC-ODBC Bridge Server does not need DNS working on your network. However, if you enable the ODBC-ODBC Bridge configurable parameters "ReverseLookup" then the ODBC-ODBC Bridge server will perform a reverse lookup on the client's IP address to obtain the client machine name. In this case, DNS must be working and your resolver library must be able to do the reverse lookup, otherwise the connection time will take much longer.
The ODBC-ODBC Bridge client only needs to resolve a machine name into an IP address if you set the Server attribute in your DSN to a machine name. You can avoid this by referring to the server machine's IP address instead.