Apple - Does the iPod Nano 6G use the headphones as an antenna?

Yes it does. From this Apple KB doc:

[The] iPod nano uses the earphone or headphone cord as an antenna, so you must connect the earphone or headphone cord to the iPod to receive a radio signal.

Most tiny radios use the headset as an antenna, and as Apple points out explicitly, so do they.

Regular speakers and other earphones would work similarly, though perhaps not as well as the pair that came with the nano, as it likely has a specific length to best pick up FM transmissions.

All wires receive radio signals, and depending on the configuration and length they are better or worse than other wires. In the case of the nano and similar FM radios that use the headphones as antennas, they use filters to couple the captured RF from the headphones into the FM receiver. The filters usually consist of inductors and capacitors and permit only the RF energy to enter the FM receiver, while blocking the speaker output from the audio driver.

The audio driver may have similar filters that block out the FM energy from the audio driver. The speakers are natural filters - they won't react to signals much above 20kHz, and the radio RF is too small to make a difference even if they did perform at 95MHz.

The cable company does the same thing when they send digital TV, analog TV, phone service, and internet to the user, and the user sends back pay per view requests, and internet and voice data. They all use different bands of the total cable bandwidth and they are separated by filters on each end so the right data gets to the right spot, even though they all share one wire. If you have DSL internet service and take the filters off your phones, you'll notice additional noise on the line - because you are now letting the phone receive the DSL signal that was blocked by the filter.

Yes.

From the iPod nano manual (page 29):

[The] iPod nano uses the earphone or headphone cord as an antenna, so you must connect earphones or headphones to iPod nano in order to receive a radio signal.

Where is the Antenna?

Where is the antenna? How can I get the best possible radio reception?

The iPod Radio Remote uses your earbuds as an antenna. For best results, connect your earbuds to the headphones port on the iPod Radio Remote and extend/unwrap the earbuds cable completely. If you connect your earbuds to the headphones port on your iPod, the iPod Radio Remote will not be able to recognize it as an antenna.

[source: iPod Radio Remote - Frequently Asked Questions]