I think there are various ways you could do this, but here is how I would implement what you're wanting. You mentioned that admin staff are reviewing each survey response. I'm going to assume they are reviewing the survey responses in a web map.
As you mentioned, add some invisible columns to your survey that will not be visible in Survey123, but they will be visible in the feature service that will be used in the web map.
One thing to consider though are the permissions of the feature service of the S123 form and the accessibility of viewing it in a web map. If the feature service is also public facing, then you will need to consider if you are okay with those fields being visible to the public (and also potentially editable). If you are not okay with that, then you have a few options. You could unshare the feature service. Or, if the public needs access to that feature service (to be viewable in a web map), depending on your needs, you could change the settings to show only records that specific end user has created. Or, you could keep the feature service unshared, and then create a feature service view and just remove those hidden/admin fields from the view, so they are not viewable to the general public. And then only share the feature service with all of the fields to your admins.
It's hard to say what the best option is for you since I don't know what your requirements are, but those are some options to think about.
