Nevermind! If the credentials you use in the External Data Sources are set up as a user in Filemaker Security, the ODBC access will work regardless of the IWP login.
I think I tested this, but apparently had not been logged out of IWP long enough for the credentials to reset.
Using external ODBC data sources in Instant Web Publishing
To support authentication with an external ODBC data source in Instant Web Publishing, you must store the user name and password for the external data source in the FileMaker database.
Note ODBC data source single sign-on is not supported in Instant Web Publishing.
1. Open the database.
2. Choose File menu > Manage > External Data Sources.
3. The Manage External Data Sources dialog box appears.
4. Select the ODBC data source in the list and click Edit.
Chapter 3 | Working with FileMaker databases on the web 25
5. For Authentication, select Specify user name and password (applies to all users) and enter the user name and password for the external ODBC data source. (Make sure this username and password set is also in Security)
6. Click OK.