Irradiance volume

Irradiance volume on Eevee seem to only bake the emissive materials, it does not bake global illumination, is this the intended effect ?

For example the cube color does not project on other polygons, because the irradiance seems unable to compute lighting bounces.

Aslo the baked map does not look very good for baked AO or shadows it produces, is there some parameters to increase qulality to make it more acceptable ?