In your case any fault that comes before the wires enter the gfci will not trip it. If the gfci is on a dedicated branch circuit and that gfci is all that is on that circuit.... then if nothing is plugged into that gfci and it trips when you power up the circuit breaker then it almost has to be miswired.
Your circuit breaker will not trip unless you have a sort to ground with the hot wire or a short to neutral with the hot wire in your situation. A fault that trips a gfci will generally be a very small leakage of current in the milliamps range this will not trip a circuit breaker.
The situation I described earlier would only apply to a cable wired to the load terminals of a gfci that was protecting a down stream regular receptacle.
Please look again at the way you have your gfci wired.
Installing a regular receptacle and plastic box only proves that something was wrong with the way the gfci is wired.
There was tape over the load terminals of the new gfci's correct?
Was your gfci wired like this one in the image. The line terminals are across from each other not diagonal or any other way.