In Michigan, daycare licensing requires that there be a suitable bed/cot for each child, specifically a pack-n-play or crib for infants. It specifically states that children are not to sleep in carseats or other baby equipment and that if they fall asleep there, they need to be moved. I'd definitely mention your concern and if nothing changes, let the parents know.
So not acceptable. Just one reason I am so thankful I can afford a licensed daycare and refuse to leave my DD with a private sitter/day care. You just don't know how they are really taking care of you child! At least I can watch my DD throughout the day online and there are people watching those that are watching my child.
I would want to be told if I was a parent of one of those kids. So not acceptable.