No, and that's a big problem. People with mental illness, especially those whose illness has made them homeless usuyally have had very traumatic interactions with police whose lack of training in dealing with the minds of the mentally ill exacerbates bad interactions. The feeling of helplessness in the police to be able to reach a satisfactory solution to the problem presented by a mental illness situation is demoralising.
Remember,too, that for the constables called out to a mental illness situation there are likely to be aware that at the same time calls are coming in for them to deal with all the other types of situations that normally occur durig a shift. There are never enough police on duty at a given time to deal with all the calls coming in. So while police are stuck in an A&E unit with a mentally ill person, some arsehole is beting his partner and some drunk has wrapped his car around a pole. Which job gets priority?
As dramatist W. S. Gilbert's lyric in The Pirates of Penzance song "When a felon's not engaged in his employment" sung by the Sergeant and Chorus of Police, "A policeman's lot is not a happy one ..."