No, you can not use FileMaker as an ESS data source. You can still use the "import from ODBC data source" and "Execute SQL" script steps to exchange data but it will not be live as with an ESS source.
You could of course use an intermediate MySQL database and have both databases work with that but even then there would be a sync delay.
You may want to reconsider and do the go-live in one painful step...
Wim is correct. You can't do ESS for FileMaker data sources.
We are in the middle of doing a similar upgrade process. We generally do one solution (however many files) all at once, then move to the next one. If you have one file that's used as a data source by multiple solutions, you can duplicate it in .fmp12 format and just keep those two files synchronized via ODBC or scripted import / export to a supported format (XML, CSV, etc.).