It can't be "doubly effective". The energy cannot simply disappear into the void. If it is used to run something electrical in the house, that energy is still there. If you ship it into the grid and across the country, less of the heating is localized. But it is still heating as it travels through the wires.

As it turns out, solar panels are often more reflective than the typical roof of a house in North America. So solar panels can actually reduce the heat island effect. But it is mostly independent of whether they are hooked up at all.