Is there a quick, low-impact way to determine whether a Teradata table is empty or if it contains rows and you don't always know the column names or indexes?

You came to the right place for help on this. Next time you need to know whether a table is empty or not, try this:
SELECT 1 from table_name SAMPLE 1;

If the table contains rows, the statement will return immediately after sampling one row from the table. If the table is empty, you will get an indication that no rows were found.

What SAMPLE n does is take the value specified by "n" and dip randomly into the table to select "randomly" that number of rows. Because you do not care about having meaningful data returned, "1" is selected in this example just to provide something as the object of the SELECT and to eliminate spool file processing. This query will be as short in duration whether the table contains rows or not.