Yes, because the traction control uses the ABS system, so you have to fix that first, and then everything should be fine.
On my 1992 with auto. trans. and no traction control, they came with a limited-slip rear differential---that was their traction control! Also, they have a 3-channel ABS system (front left, front right, rear) because of the LSD. That's why cars with traction control can't use mechanical LSD's, because they would interfere with the traction control mechanism, which uses the ABS to slow the wheel down from spinning---which requires a 4-channel system.
So by having traction control, you're using the ABS system to stop wheel spinning. If it doesn't work, neither does your ABS system---not because the ABS system is faulty, the traction control system is!!!