Matt
You're not banished to a desert island, but I'm not so sure that you will really save any money over purchasing the rocket kit by the time your done with the project.
You don't have to glass the Binder Velociraptor kit for strength. You might want to checkout my comments from the scratchbuilt part of TRF
https://www.rocketryforum.com/showthread.php?s=&threadid=6509
If you're set on trying PVC here's some comments.
First, I have to say I don't like the use of PVC for motor casings. PVC is rather brittle and if a motor CATOs, it is likely to send plastic shards all over the place. For an airframe however, it's a different story since it's not pressurized.
The PVC I'm assuming you plan to use is the non-pressure rated gravity drain type. In the 4" size the wall thickness is 0.070" which is comparable to QT. The density of PVC tubing is about 1.38 g/cc which is about 1/3 more than a typical polymer like ABS which is 1.04 g/cc. It has a 4.075" I.D. compared the QT at 3.900" I.D.
I don't think mechanically there would be a great difference between the two. QT is ok for run of the mill rockets that will not exceed M=0.85, and can not be glassed. (Ref PML website) I don't know the composition of QT however if you go to
https://ww.matweb.com/ you can get the mechanical of virtually any polymer. My speculation is that the PVC is slightly stiffer than the QT, but I don't have any hard evidence for this.
Gluing to PVC and any other smooth extruded plastic is tricky. At a minimum you have to abrade the surfaces. A nonabrasive scrubber, Skotchbrite(R) or steel wool will work. Some suggestions for adhesives are listed in this thread.
You might consider going all PVC using PVC sheet for the fins and bulkheads. This greatly simplifies the construction and permits the use of standard PVC primer and cement. It will make a bond that is as strong as the material itself. No epoxy or CA required. [Note: PVC primer and cement is a solvent cement (that mean it disolves the surfaces and when the solvent evaporates you are left with one solid mass) will only bond PVC to PVC. It will not bond anything else to PVC]
Also 4" standard PS nosecones will work with 4" PVC. Just build up a masking tape layer to make up the 0.175" diameter difference.
Lastly, all polymer airframes will be effect more by heat than cardboard or phenolic tubes. Do not use a piston ejection stystem. Instead use a Nomex(R) parachute protector. If you keep the airspeed down well below Mach, the non-presure rated PVC pipe should be ok.
Good luck.
Bob Krech