I agree that gophers are generally evil, little rodents.
I have run black poly pipe to my trees in my drip irrigation systems. I just ran it on top of the ground, but it has been chewed through in several locations. Presumably by gophers, but I have several other types of chewers on our property.
I do not know if they just wanted something to chew for their teeth, or if they were trying to get at the water inside the line during our drought periods? I have some PVC manifolds at the start of a few of my systems, and there are zero chew marks on the PVC.
Personally, I think you could use PVC in your air pipeline system. However, that is against "code". PVC pipe is designed to deliver fluids. Steel pipe and poly pipe just split when the burst strength is exceeded by a gas. PVC will actually shatter.
However, I would NOT be worried about (mostly) buried PVC in a low pressure situation where humans are rarely around the pipe.
The burst strength on 3/4" SCH 40 PVC is 1540 psi. The rated working pressure (for liquids) is 179 psi at 100 degrees F. Your systems should operate MUCH below that pressure.
PVC pipe does significantly de-rate with higher temperatures. I might consider putting a bit of steel pipe right at the outlet of the compressor for two reasons. First, that pipe will radiate away some of the heated air coming off of your air pump compressor. Secondly, you do have your face at that location more than just rare occasions when you check the pump, read the gauge, etc.
I also agree with esshup about that being a LOT of glued connections. I would definitely put a valve on both ends and pressure the system up to 50 psi overnight and confirm that it held pressure perfectly before burying the pipeline.
My odds of 100% leak-free connections does go down when I move up from 3/4" PVC. 1" is still pretty easy, but 2" connections are definitely more difficult.