Hi,
thanks for your question. No, this is not possible, sorry. TablePress can only use its custom data format from its own data source (“Custom Post Types”).
You could of course export the mySQL table to CSV and import that into TablePress – but you would obviously lose the realtime aspect.
Therefore, the best way for you should be to use a custom PHP/mySQL implementation, e.g. in a WordPress Page Template. You can then add the advanced functions manually, by integrating the DataTables JavaScript library (see https://www.datatables.net) directly. This is the same JS library that TablePress uses.
Best wishes,
Tobias