Typically, you will not be hospitalized unless you have means/plan. Suicidal thoughts are often a part of depression and many other mental illnesses. Most therapists know to expect them at times. But that does not mean that he/she might not over-react.

If you think you are in any type of danger of actually following through with your thoughts, say that. If they are just thoughts, say that. Thoughts are scary but can be changed. That's what therapy is for.