The Child Behavior Checklist by Connors is only one method of evaluating for ADHD. Is the school recommending any other evaluation tools? There is no medical test for ADHD. There is a TOVA test (test of variable abilities), but that is usually obtained through a neurologist or ADHD specialist. If your son receives the Wechsler Intelligence Scale for Children test -- that contains a freedom from distractibility score that would indicate any attention problems.
I suggest that you speak with your doctor and see what he or she recommends based on their medical opinion. Take this reply with you. If it is decided that your son needs ADHD treatment, then make that decision based on his total needs, not just on the gifted program. I do not think it is right to exclude your son from the program based on attention behaviors. The advanced program may end his inattentiveness! If it becomes necessary for you to push for your son to be tested so that his educational needs may be met, you may have to seek outside professional testing to learn the full range of his abilities. Good luck.