Yes - I got one yesterday.
Here is a except from the 5G user manual (bold emphasis mine):
"iPod nano has a built-in FM radio that displays station and
song information, lets you pause live radio, and tags songs
that you can preview and purchase in iTunes.
To listen to FM radio, connect earphones or headphones to iPod nano, and then
choose Radio from the main menu.
iPod nano uses the earphone or headphone cord as the radio antenna. You must
connect earphones or headphones to iPod nano in order to receive a radio signal.
The radio doesn’t play through the iPod nano speaker."