In my spreadsheet budget, I have 3 categories: saving, bills, and credit cards (spending). When I was paying off my student loans, I had a sub-category underneath bills that was "Additional Student Loan Payment." So I guess it depends on your categorization and definition of saving/spending.
How I define a savings contribution is if it increases your tangible assets. In this sense, the payment would not fit because you are not increasing your assets, you're paying down a loan.