I’m not sure if it helps keep your average hours. But. It does protect your absence and in some states they cannot hold an absence covered by sick pay against you when it comes to conversations and coachings.
Good question. Unless there are state and local laws on this, I think sick leave and vacation are not part of your "average hours worked" because those are not actually "hours worked".
But here's a good Target Jeopardy question: if you end up with a lengthy amount of sick leave or using up a bunch of accumulated vacation, are those days away from work mathematically excluded from the calculation formula for "average hours worked"?