Typically on a Y connected secondary transformer winding, the neutral current should be equal to three times the zero sequence current on the feeders, so yes there will be current. But I would not call it stray current. It is the current to serve the unbalanced single phase loads on the distribution.
Opening the X0 lead will make the voltage rise on the X0 bushing, and what ever is attached to it. This voltage will be up to the voltage on the phases, depending on how unbalanced the load is.
This is the danger point, because we expect there to be some current on this.
On rectifier transformers, the current will be there because of the harmonics from the rectifier, as in many cases the transformer is part of the harmonic suppression.
The current between the transformer case, or core ground and the ground grid is actually stray current. And should be small.