Run 6 AWG NM-B cable through 1 1/2 PVC pipe indoors
The central vac PVC isn't listed for electrical use, so it won't fly as a conduit or raceway for electrical wiring.  

But you aren't really using it as a raceway, just as a protective sleeve for the cable, so you could make the argument that if the cable could travel the same path without the pipe, it should be able to travel that path in the pipe.  

The main sticking point would be the bends.  You might have a very hard time pulling the cable around those bends and T's.  The resulting install may even violate the bend radius requirements for the cable.  If you cut out the elbows and T's and use those spots as pulling points, that should get around that problem.  

You'd want to be sure that the pipes are protected by nailers where they pass through framing closer than 1-1/4" from the finish surface.  That could be a gray area.  You might assume that was the case when the central vac was installed, but if you're repurposing the pipe, your local code enforcement department may insist that it be re-inspected, which would mean removing the finish (drywall).