Hi @Atalanta
Welcome to the Forums.
Any mental health phone service will have in place a protocol of when and why they will contact emergency services. At the point the police will make a decision as to whether they have reason to break privacy and to trace a call. As there are strong privacy laws, police have to be very certain there is an imminent risk of safety - so it's not taken lightly.
I'm also not a tech guru - so I can't answer the question with certainty. All I can say is that it's the services responsibilty to follow protocol if they feel there is that imminent risk. The service will hand over to police all the information they have (which may or may not be correct, if you're giving a fake name for example) and it's over to them to make the final decision. Due to the privacy, (as far as I know) services do not report back any information (ie: whether they in fact trace the person or anything related to the outcome)
Also, as a FYI, each state has its own process. Just because the police are called, doesn't mean it will be the police that are sent - it could be Mental Health Crisis Assistance and Treatment Team (CATT) or an ambulance, for example.
Sorry I couldn't give you the specific yes/no you are after, but I have shared everything I know.
Take care,
Nik
PS: I just came across your post in the other discussion topic which is the same question. I will remove that so you have all the responses in one spot.