Well, not really "automatically". But if all you want to do is add a watermark to video clips, you can do it faster with Compressor. In the Inspector window, the Fitlers section, the Video tab, at the very bottom of the video filters list is "Watermark". Add one, adjust, size, etc. Save that as a Custom preset first. Then save that out as a Droplet. You can then drag and drop a folder full of videos on the Droplet and it will add the watermark in the background. I hope this helps.
Here's the Compressor user manual page, at the bottom is more info on the Watermark Filter.