Is it possible to automate the configuration of Action permissions with something like PowerShell?

It is not possible to automate the configuration of the Action permissions with PowerShell. There is an NWADmin command called ConfigureSettings that is part of the 'NintexWorkflowSetup.xsd' which can automate the configuration steps after the install of Nintex workflow. This is however very high-level and is only at Farm level, not at site collection/site level.