Overall, I did click Save last night! I had to give it a name “My Custom Modifiers” which created it under Custom Modes list (it certainly does save the information to your user data) meaning if you want to remove it from your Custom Modes list deleting your user data files will remove it
To use your custom saved modifier! Load up a Private Match, click on Modifiers and select from the Custom Modes list your saved modifier mode and click back “Note” where is says on the above screenshot “Classic Hunt” if selected your custom mode your name will appear here confirming your selection
I also noticed that if you wish to make changes to your custom saved modifier, after clicking save you must choose it in the list of your custom saved modifiers or choose to create a new one
I was right in a lot of way! Even when I did not test it myself, but NOW I can confirm that it does save to your user data as I first assumed