Can I model polyethylene plastic pipe using Caesar II?

Is there any reason I can't just enter the material properties in as a new material and model as normal?

The quick answer is yes, you can enter material data in CAESAR II to model the response of plastic pipe to various loads.

B31.3 paragraph A319.4.2 - Formal Analysis Requirements (for nonmetalic piping) states "If substantially elastic behavior can be demonstrated for the piping system [see para. A319.2.2(a)], methods outlined in para. 319.4 may be applicable" in analyzing the system. So, if your system acts like a metallic system, the CAESAR II analysis should give numbers you can work with.

But see also para. A319.2.2 - Displacement Streses where the Code discusses elastic behavior and overstrained behavior. Here, too, you will see that the Code says the designer "shall establish safe limits for computed stresses". To me that means that the CAESAR II code stress checks should not used.