No the price of your room doesn't matter, as long as you're staying at Disney you can purchase the dining plan. The "rack rate" think is only for free dining plan which comes up as a bonus from time to time (instead of discounting their rooms by $40 in the off-off-season like most hotels, Disney keeps the room price the same but offers you free dining).
When it's not free, the dining plan costs $38 per adult and $11 per child ages 3 to 9.