There is no way for anyone here to know how your therapist will respond. They all vary when it comes to this sort of thing. I have had bad experiences with past therapists around this topic, so when it is serious, I keep it to myself. But that's me. My current therapist has never said what her policy is, but her voicemail states to go to the hospital, so I have come to some peace and acceptance that I travel alone when it comes to this issue. (I do share when I'm down, however, just not if I have plans or means.)

Others will have different experiences, though, so if it's a concern and your therapist hasn't said, you might want to just come out and ask.