Are you allowed to carefully tape conductors (bare) together to establish a connection in a control panel or would the NEC approve of something like this?
No. Article 110.14(B) requires joining "with splicing devices identified for the use or by brazing, welding, or soldering with a fusible metal or alloy."
Thats one I don't agree with the NEC on. If its control cable, I would just as soon twist the wires and tape them than use a wire nut. Of course, soldering or other methods are even better than twisting and taping.
jghrist,
I would use insulated connectors if I were putting them on but I have seen to many that were mutilated by the electrician installing them. 6 of one and half dozen of the other.