To upgrade from S class, you will need to pay 20,000 miles and a $500 co-pay. Sounds like a lot to me. Just for reference, from the FAQ:

From continental US to Europe:
From C or D class: 20,000 + no co-pay
From Y or B class: 10,000 + no co-pay
From all other Economy classes: 20,000 +
$250: M, E, U
$350: H, Q
$400: V
$450: W
$500: S, T, L, K