67 Camaro, Is it possible to pull the radiator frame / support out of the car without also removing the front nose or lifting a fender?

Thank you.

I guess I can't speak for the 67's, but I removed mine on my 69 without removing any of those items. I am not positive but I think 67-69 use the same core support. It's snug but can be done.

67,68,69 use same core support.
Yes, you can remove it without removing sheet metal, but I would put supports under the fender extensions. With grill and sheet metal there is a lot of weight on the firewall bolts and you could wind up having to re-align your sheet metal. You could also do some sheet metal damage at the fire wall.
Bob C