Why do you want to do it? What do you expect that it will happen? Do you think that they are not taking you seriously? It could help, but I'm not sure if it's that useful. After all, in therapy you need to talk about your problems, your traumas, your fears, etc. I feel like, if you think that this is going nowhere, you should simply tell them that. That you feel like therapy is not working and you may need change the way that your sessions are going. They may tell you that it's too early to say (three sessions are not much, after all), but it's something important to mention, I think. If after several sessions more you are still not feeling anything, maybe you should talk to them about changing to another therapist.
But about your question, yes, you can say that you sometimes think about suicide if you want. It's unlikely that they will send you to a psych ward if you don't talk about plans or about being scared of doing it impulsively. After all, the psych wards are not big enough for every suicidal person.