First, be careful with the parentheses count/placement, in your first example you have a closing parentheses after the column variable, which would break the entire calculation formula.
Next, the ROW() function you're using only works when the calculation is within the table because that value is basically a reference to the index of the "current" row in the table. You should only use ROW() for INDEX functions that are inside of a table/collection.
If you're only trying to check if the first row is empty, you should replace ROW() with 1, because INDEX(Table.Column,1) will tell the formula to get the value of the first row.
Additionally, you do not want the INDEX function in the sum because INDEX retrieves a specified row of the table, but for the sum you want every value.
=IF(INDEX(Supplemental_Calculation.V_1__Actual_2022_Gross_Receipts,1)<>"",SUM(Supplemental_Calculation.V_3_Amount_Due),"")
Another option would be to check if any of the rows are empty, which you could do with COUNTIF
For example =COUNTIF(Table.Column,"=") checks for empty fields, meaning you could make the IF statement check if the resulting value is less than 1,
=IF(COUNTIF(Supplemental_Calculation.V_1__Actual_2022_Gross_Receipts,"=")<1,SUM(Supplemental_Calculation.V_3_Amount_Due),"")