Very few do - some have vets that are 'on call' and sleep on the premises, checking on the animals throughout the night, but most do not have this facility. It tends to be the larger 'hospital' group vets that provide this service.
I would be reluctant to leave an animal in overnight unless I was sure there would be someone with them - I lost a dog once who died during the night, and I wish I had taken her home where I would have at least been with her. Of course this is not always possible, if they have to be on a drip for instance. Check with your vet, or phone round the other vets in your area.