Yes. I have attended far too many road traffic accidents where a loose dog has been rattled around a vehicle at forty miles an hour, killing itself and the occupants, despite them being strapped in by seat belts.
I still occasionally see Cockers sitting on the rear window ledge.
Even a minor shunt would result in them hitting the back of your head before exiting through the windscreen.
And I?m not even going to mention the nutters who drive about with their dog half hanging out the window.
Incidentally, we hand out car stickers to our clients, stating the number to be phoned for veterinary care in case of accident. They give a bit of peace of mind.