Does the tailwind component always have the same absolute value as the headwind component?
YES, If the "amount of headwind" was 10 knots due to the crosswind, then the "amount of tailwind" would also be 10 knots on the reciprocal course. 

BUT, because the 10 knot disadvantage with a head wind will last for a longer period of time than the 10 knot advantage with a tailwind, the entire trip will take longer and use more fuel than a trip in still air.

EXAMPLE: The headwind leg is 15 minutes longer, but the tailwind leg is only 10 minutes shorter, so you have a net loss of time.