No, the ipod video has different hardware to the ipod nano, so it won't work.
Rockbox is a replacement firmware for your ipod, if you install it, then you can use Rockbox to play videos on your Nano.
However, the video format supported by Rockbox is different to the format Apple supports on the ipod video. For details of how to play videos in Rockbox and how to convert your videos, see here:
http://www.rockbox.org/twiki/bin/view/Main/PluginMpegplayerFor instructions on installing Rockbox, click on the "manual" link in the left menu on this website, then select the manual for the Nano and carefully follow the instructions in the Installation section.
You may also find the FAQ helpful:
http://www.rockbox.org/twiki/bin/view/Main/IpodFAQ