Can I Update a Table with a button push

The table is the result of a SQL query. And rather than run the query on some sort of timed basis, can I simply tie a button to it to “Refresh” or re-run the query?

Just set the query to relative or absolute poll

https://docs.inductiveautomation.com/display/DOC/SQL+Query+Binding±+Polling

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Yes. system.db.refresh()
Although it is documented to refresh non-polling SQL queries, it actually will refresh pretty much any binding to property.

Or if you want to manually refresh the table run the following code
Where Power Table 1 is the name of your table.

system.db.refresh(event.source.parent.getComponent('Power Table 1'),"data")