Does anyone know if it is possible to publish a "public" survey that is only available to members of my organization that have a named user account regardless of their User Type?
There are a few situations in our organization that it would be nice to get feedback from our named users with a User Type of Viewer. Some examples are signing up for GIS training, reporting map quality issues, or just giving Viewers the ability to provide feedback about ArcGIS Online/Portal.
If it's publicly shared so that non-Creator users can add features, it'll have to be exposed to the public as a whole. We use surveys like that for similar situations as you describe and we just make sure the link is only shared with the intended recipients. We've never had issues with spamming, thankfully.
An extra measure you can take to protect your layer is to create a view layer that filters all data where "created_user" is not equal to "Esri_Anonymous" (assuming editor tracking is enabled on the layer). That way even if someone did submit fake entries, you wouldn't even need to see it.
Also, you can embed the survey into a dashboard, and then restrict access to the dashboard to org members only. We've used that method, too.
None of these are foolproof, of course, and anyone who opens the developer window of their browser can see and copy out the itemID / URL of the layer. You just have to assume that most people aren't going to go to that sort of trouble to spam your surveys.