Yes you can. Please see the article Startup Python Scripts in FME. You can find these articles via the Knowledge Base.

No, this only allows the user to copy and paste python script into the Startup Python Script. I want to actually run a .py file and corresponding config file like I would from command line. Maybe I can write a python script to run a python script, but would prefer way in FME to actually run the .py file.

"In the Workbench Navigator pane under Workspace Parameters > Scripting, you will see a parameter called Startup Python Script. Right-click on the parameter and select Edit Parameter Value to open a special Python editing window. Here you can enter some Python code that will execute before the translation but after the execution of scripted parameters."

A creator, into a system caller with the path to the python script specified would partially achieve it. It won't run it before the FME process kicks off, but it will be the first thing to run