Sure, you can do this. You'll need to hook up a 'select' event listener for the GeoChart that gets the state and filters the data used to draw the Table:
/*
* assumes:
* data is the DataTable used to draw the GeoChart
* tableData is the DataTable containing the data for the state
* state is in column 0 in both tables
* tableView is a DataView based on tableData, used to draw the Table
*
* this can be simplified a bit if the DataTable used for the Table
* is the same one used for the GeoChart
*/
google.visualization.events.addListener(geochart, 'select', function () {
var row = geochart.getSelection()[0].row;
var state = data.getValue(row, 0);
var rows = tableData.getFilteredRows([{column: 0, value: state}]);
tableView.setRows(rows);
table.draw(tableView, options);
});