Can I install wiring in the space used by a sealed air duct and PVC water supply lines?
Yes you can run electric in any interior wall.  You cannot run electric inside of water supply lines, inside duct, or attach electric to either.  

The cavity you describe is common in a lot of house layouts.  I have a 8 foot section that is about 12 inches wide in the middle of my house.  It has duct work, main stack and tons of plumbing, with plenty of electric too.