Surely an overlay approach without the raw data becomes an RNAV approach?
No, an overlay approach generally doesn't require the underlying NAVAID (NDB or VOR) to be serviceable. That's the case in Canada. But we're talking about a lot of countries here so you'd have to check your country's regulations.
My understanding of an overlay is simply that you are saying to the AC that you can't be bothered to manage it yourself (selected/selected) so please will you do it.
You're thinking of an FMS doing the overlay approach. And possibly calculating the 3 degree path for you. You only need a GPS to do a GPS overlay approach... no FMS required.
But the primary source of NAV data is the raw stuff. So if it's not there, you can't do it.
Not true! Again, speaking from Canada but I think most countries have the same rules. When an overlay approach is allowed, you do not require the underlying NAVAID (raw stuff) to be operational.
The whole point of an overlay is to make the primary source of navigation a GPS instead of a VOR or NDB!
When there is no overlay published then your primary source is the raw data and you must follow it even though you really should be setting it up on the GPS or FMS, as I detailed in my post above.