How to execute a Parallels Windows application with command line parameters from Mac?
APPROACH 1

This approach is a hack, but works with the least expensive version of Parallels. 

On the virtual Windows machine:


Create a *.bat file for each possible set of parameters. For example:



     @echo off
     start "" "C:\Program Files (x86)\MyApplication.exe" --myArg
     exit


On the Mac:


Navigate to $(HOME)/Applications (Parallels)/VMNAME Applications, where VMNAME is the name of a virtual machine.
Duplicate the MyApplication.app application bundle and rename the duplicate MyApplication --arg.app.
Right-click MyApplication --myArg.app and choose "Show Package Contents*.
Open Contents/Resources/AppParams.pva in an editor (e.g., TextEdit), and change the value of the App Path property to the absolute path in the virtual machine to the *.bat file, rather than the application. Save the file.


This is similar to @johnl's answer above, which provided the vital clue. However, at least in Parallels 11, the App Path property would only work with an application path, not with a command line.

APPROACH 2

As of Parallels 11, this approach requires one of the more expensive editions of Parallels - Pro or Business. I don't have either, and haven't tested this approach.

According to the Parallels manual Parallels Desktop for Mac Pro Edition, the command prlctl exec can accept a command to be executed on the Windows virtual machine.


  prlctl exec
  
  Executes a command inside a virtual machine. Parallels Tools must be installed in a virtual machine to use this utility. Commands in Linux guests are invoked with bash -c.
  
  Syntax
  
  prlctl exec vm_id|vm_name command
  
  Parameters
  
  Name Description
  
  vm_id|vm_name The UUID or the name of the virtual machine.
  
  command A command to execute.