Requiring a Snap

Is there any way to get Rhino into a mode where it will only accept snap points?

Ie, If I click and Rhino does not think I am on a snap point, it will ignore it.

Do you mean Grid Snap or Object snap?
Grid Snap yes, provided you don’t override it using an Object snap.

Object snap only, no. It there’s no object with a persistent property in the selection range, the osnaps are ignored and you get the point you click.

I was intersted in OSNAP. I guess this would be a feature request.

No. If you click at a point prompt, you will get a point.
That point can be refined using Grid snap, Object snap, or elevator mode options, but it will always get a point.