Kristie:
The following technical articles most closely describe how to make the change you are looking for in the *.loc.xml of the locator built with the Create Address Locator tool. You would want to search for the "Suffix types" section and add 'PW' to the list of aliases for Parkway if you want that abbreviation recognized. We do not recommend modifying the the xml of the locator, but if you do, Tech Support wouldn't be able to provide help in maintaining the customized locator.
How To: Add a custom highway to the address locator style
How To: Add city aliases to the address locator style
Given that you are transitioning to ArcGIS Pro, I would suggesting building the locator with your existing data using the Create Locator tool using the StreetAddress role to see if that resolves the issue. The locator created with the Create Locator tool in ArcGIS Pro cannot be used in ArcMap unless it has been published as a service from ArcGIS Pro.
-Shana