No, an ambulance officer would not administer a sedative. It may be different from place to place, but sedatives are not on the list of medications that ambos are allowed to administer. The police NEVER administer medication. Even a doctor would be unlikely to medicate if the person was just shouting and screaming - they would try to find out about the persons medical history, particularly what other medication they are on, what their health complaints are etc Sedatives can interact with other mediactions and cause real problems.
In reality, maybe people would ignore them and they'd would exhaust themselves and quiet down. Or maybe someone would call the police or an ambulance. If they called the police, the police would try to calm them down, find out the cause, but if they couldn't they would get an ambulance since they would assume that there was some psychiatric reason. The ambulance would try to calm them verbally, but if they continued they get them to hospital - in the police car (if they couldn't get them into the ambulance) or otherwise in the ambulance. Depending, the hospital would send them to psych if they keep screaming. Psych would lock them in a room and contact relatives to find out the persons history.