Would a doctor/psychiatrist be accepting if a client left all treatment with everyone after an offer of an inpatient stay to stabilise symptoms pls ?

Not unusual: Without knowing specifics of the case, it is not unusual for a patient/client requiring a higher level of care, necessitating an inpatient stay, to discontinue outpatient care. That being said, if the outpatient care prior to admission was appropriate, the patient/client would likely return to those services as part of their discharge plan. This is of course, in the context of mental health.