Yes, I think that is the difference between deep conversation in the sense of sharing more personal issues with someone else and another kind of deep conversation that can be disturbing for some.
I think the stereotype of existentialism causing unhappiness is because when you want to look at reality squarely in the face and get to know it, you cannot have the ordinary things that protect you from being aware of it, like your preferred entertainment, chatting to friends, etc. even if you talk about really deep personal stuff.
The happiness lost is just a superficial kind of happiness anyway though. You can gain a much more secure kind of happiness if you can somehow come to terms with the existential questions, at least that is how I feel about it.