It seems likely. Given that the copper atoms prefer to form a non-superconducting material, it makes sense that there would be regions where the energy is just right to form the correct structure, and you get the incorrect structure everywhere else.
Given the way crystals grow, it then would follow that you'd get discontinuous crystals or grains within the material.
If we're taking bets, my money is on this exact thing happening. It'd explain the inconsistent results we've seen so far.
Could there be small pieces of RTSC inside the sample (causing the floating)
But then enough impurities to not be able to complete a circuit through the sample?
And cooling makes other parts of the sample super conducting?