This simulation should over estimate this effect considerably. It only used parallel wires in one direction. The actual screen is a grid with wires in both directions. This would make the leakage field between wires much smaller.
This model does show that electrons of slightly lower energy than the screen voltage can pass through. This effect could partially account for the 1V offset seen in gun energy. This model shows that about 50% can get past the screen at 0.5eV below the screen voltage but most paths are badly deflected and probably would not reach the anode.