Yes, now we can publish a video along with the product on Etsy through the App.
We have to just import the product in the App with a video in it and simply publish it on Etsy through the App. Just make sure that the auto-sync of the "video" should be enabled in the settings section of the Product Management, in Settings.

NOTES;
Bring your product to life with a 5 to 15 second video - it could help you drive more sales. The video won't feature sound, so let your product do the talking!