How to setup Unity to import .max files when max is activated using a network license?

I am able to open max files via double-clicking the icon in windows and max will load completely but when I try to import a .max file using the Unity import new asset dialog I am advised that max will not load and that my trial is expired.

Does unity support copies of max that use a network license?

Max files are absolutely massive to import into the unity editor. What you need to do is export it out as an fbx with embedded media. Unity should then import the file easily and with all the textures intact. This will make then a better import as unity understands fbxs better.