You didn't specify how you manually start the process (from cmd, explorer etc.) but this could be related to the working directory being different.
You could try adding the -WorkingDirectory parameter to the Start-Process line:
start-process -FilePath "\\servername\Data\QuickCrpe\QuickCrpeReg.exe" -WorkingDirectory "\\servername\Data\QuickCrpe" -ArgumentList '/S'
There are plenty ways to pack a PoSh script as installer or binary. Inno Setup for example would allow you to create a installer.

