I'm not sure I understand. What kind of object are you describing?
In general, however, if you have a GFCI device, it might trip someday. Someone is going to have to gain access to the device, in order to reset it. If that requires turning off and tagging out the object, and using a screwdriver to open the object, that would be inconvenient. But I don't think there is anything in the NEC to prohibit it.
Is that what you were asking?