Can Fake iPods Play Video?

In short answer yes. But the real question you want to be asking yourself is "do you really need to watch video on your fake iPod". The video quality on most fake iPods isn't very good but even if you have struck gold and the video playback is good you might have to convert your files to a crazy unknown format so that they will work on your fake iPod. 

If you have a touch screen fake iPod there might be a company name somewhere on the device. Check out their website and help sections if such exist and play around putting videos onto your fake iPod. 

When I was using my fake iPod I would convert my files to down to a smaller resolution before changing the videos into some weird almost unknown format before uploading them manually onto my device. The video playback was so bad that I just didn't bother after that and so I have forgotten the format. 

Good luck uploading video to your fake iPod in the future!