Is there a required spacing between waste vent line and chimney?
The ultimate standard is going to be your local building department and inspector, but the International Plumbing Code only specifically prohibits plumbing in elevator shafts or in elevator equipment rooms (301.6).  The only requirements specific to location of venting deal with size, distance, and type of connection to the system that they are venting. Everything else is deferred to the International Mechanical Code.

For chimneys that are used only for venting gas-fired appliances, the IMC defers to the International Fuel Gas Code.  The relevant portion (501.15.4) of that code states only that there be airspace clearance to combustibles per the International Building Code.  Note that there is a specific exemption for masonry chimneys with a low clearance liner.

This gets you back to what it appears that you already know from your question (R1003.18) "Any portion of a masonry chimney located in the interior of the building or within the exterior wall of the building shall have a minimum air space clearance to combustibles of 2 inches (51 mm)." However, again this is exempted if a low clearance flue liner is in place:


  Masonry chimneys equipped with a chimney lining system listed and
  labeled for use in chimneys in contact with combustibles in accordance
  with UL 1777 and installed in accordance with the manufacturer’s
  installation instructions are permitted to have combustible material
  in contact with their exterior surfaces.


PVC will ignite at 435°-557°, roughly the same temperature range wood will (although it will be a molten puddle at that point). So, unless your chimney liner is rated for contact with combustibles you would need galvanized or some other form of non-combustible pipe.  If you don't know how the chimney is rated, I would take the presence of the existing air gap to indicate that it is not contact rated.

That said, if you can maintain the 2" minimum to a PVC pipe and the local code authority will sign off on it, I'd do it. Oversimplified, a 90% efficient gas furnace would basically dump only 10% of it's BTU output into the flue gas. I don't ever recall finding a brick chimney that was even warm to the touch on the outside, except right next to the inlet from the furnace.