I have the new 16Gb blue nano (got it this afternoon), and can vouch for lack of radio functionality without headphones. Leave them off, and the radio function gives a message refusing to activate without them. Plug them in, and the built-in speaker is deactivated.
Not that you'd miss anything. Honestly, the built-in speaker is too small for anything resembling high-fidelity music reproduction. Think of those old handheld transistor AM radios back in the 70s. Now imagine that, but less than half as loud at best. It's good only for a quick audio preview of video camera clips.
I didn't turn my Voiceover on, so I don't know about radio station announcing. That would be a handy accessibility feature, though, especially since Voiceover can be programmed for menu navigation. Time for some research... 🙂
EDIT: Oh, and by the way, the new nano is so worth it. I had been considering a refurb 4th gen, but now I'm very glad I waited.