It's not written 100% clearly in Street Magic, and I would assume the answer is "yes", but may as well ask opinion here anyway ...
"Does Background Count extend to the astral plane, affecting astral forms who are not materialised"
Only thought of the scenario because of the idea of a spirit attacking a (dual natured by definition) cyberzombie. The spirit doesn't need to materialise to use their powers on the cyberzombie, so it would be a really effecient way of killing them, since the cyberzombie will have a harder time fighting back on the astral than they will on the physical.
However, then it struck me - does the zombie's natural background count extend onto the astral, because that would seriously deflate the attacking spirit (potentially to the extent of destroying it).