You will need to create a system DSN, unless the QlikView service account running all QlikView services and your own are one and the same. System DSNs can be accessed by any user logged in.
Practice in many cases is creating two or more variables with the CONNECT statement, one for local and another for the server. Depending on an external factor you can measure in the QlikView script (the computer name, the user running the app, a file) it will use one or the other.
Alternatively, you can create a file named, say, "ODBCConnect.qvs" in each computer the QVW has to be reloaded with the correctly configured CONNECT statement. The script will refer to this file using $(Include=) and will always get the correct connection string.