Hi Will,
Just got confirmation and was told that this isn't possible.
Per our developers:
"An object or table that wants to participate in full-text search must implement and register an instance of the DocumentProvider interface to instruct the search indexer about details like: what content should be indexed, high priority vs low priority fields, fields that should be stemmed vs. fields that represent identifiers, search result title and summary, tracking of rows that need to be indexed, behavior when the index is deleted, etc. This requires Java code."
The only feasible workaround they suggested to index an arbitrary table without writing code is to use a list, which the list designer provides indexing configurations.
https://www.labkey.org/Documentation/wiki-page.view?name=editListDesign
Regards,
Jon