Only if you have signed consent and direction for them to be notified (and that might not occur right away but may be in a later report to them).

My therapist always knew when I was hospitalized because I made him directly aware of my intention to go to the hospital. He did not come to the hospital (and I would not have wanted him to). I did speak to him by phone calls that I initiated while in the hospital, usually just as an update to my status for discharge and arranging an appointment pretty promptly upon discharge.