Parallels desktop virtual machines cannot communicate when Mac has no network connection
From Parallels Knowledge Base the following indicates an internet connection is required for this to work.  No idea why that would be a requirement.

Network problems in the virtual machine
Article ID: 8978
Created On: Sep 14, 2010
Last Review: Nov 24, 2015
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APPLIES TO:

    Parallels Desktop for Mac
    Parallels Desktop for Mac Pro Edition
    Parallels Desktop for Mac Business Edition
    Parallels Access

Note: Your Mac must be connected to the Internet for virtual machines to be able to connect.