Given that we already have had reports of Veterans Affairs counselors suggesting death to patients who hadn’t even asked about it, no, I think yours is a wildly optimistic interpretation of what this will result in.
A dead patient is far less trouble and expense than a live one and now they’ll be able to say, hey, that’s what the patient wanted.
Yeah, ISTM that depressed patients who would seek out medically assisted suicide if it were available to them are probably already “in the system” with a medical history of depression. Offering assisted-suicide options will not provide them any additional help to avoid suicide.
Undiagnosed sufferers from suicidal depression, on the other hand, will just continue to rely on the usual “home remedies” for self-destruction purposes without entering the medical system at all. Offering assisted-suicide options within the medical system won’t help them avoid suicide, either.