Some vets won't
This thread does seem to be a bit overworked however I have found a couple of vets -granted not too many- who will not take an animal in overnight to be seen the next day. Although if the animal is in the hospital's care they will allow it to stay overnight if needed. The reasoning being that if an animal is in the hospital overnight without diagnosis and something happens to it there have been a couple of lawsuits charging negligence. Another reason is if any animals are in the hospital overnight many if not most vets will pay someone to stay on the premises to watch over them. If you bring an animal in at night to be seen the next day they would have additional wages for the person staying there. That is why some won't take them in at night. The only exception being if they already have an animal in the hospital and staff lined up to watch them they will usually allow an extra.
My neighbor on the next farm down is an attorney and filled me in on the particulars of vet care in the city and people filing lawsuits etc.
Walk softly and carry a pocket full of treats