I think you can and should say it all. I don't think they'll hospitalize you forcibly. That would require a suicide attempt at least.
Moreover, they know how it oworks, if you are really depressed, you MUST have made some tought about suicide... we all do. 15% of depressed people end up with suicide, how could we not think about it?
If you deny, they will likely conclude that you are too scared to speak the truth. Not a big problem, but trust in the docs helps the treatment.