Yes, IF (key word) you owe any back child support. In Illinois, they're stickler's for that. So if you're current, you're in the clear. If you're not, then the back is still owed.
If the court awards custody to you, or if you can come to an agreement with your ex for the kids to live with you full-time, you would not be required to pay child support. The other attorney is correct, though. If you owe back child support, you will have to still pay what you owe.