I don't think it makes any difference. The kind of pax who are going to panic will do so regardless. I've seen it countless times here, where we have the Dash 7 & Dash 8 (cockpit door closed), and Twin Otter and Caravan / Grand Caravan (no cockpit door) operating the same routes. Pax who are claustrophobic, have control issues or simply don't like being tossed around in a smaller aircraft when the bumps come, have the same reaction regardless of equipment type.
This certainly doesn't apply across the board - I am a frequently dodgy flier and I am far more at ease when I can see the pilots sitting there confidently!
I know they all sit there confidently no matter if I can see them or not, but for whatever part of my brain that can't be rational about these things, I do actually like to see them
Used to love Eastern Airlines in the UK for exactly this.