Actually, the answer is yes. Adobe Bridge has just enough functionality and can, with the use of some javascript, add watermarks to images. I have coded a script that watermarks images for me but it's specific to what I personally need. I'm currently working on making it more user-friendly and adding in various settings to allow customization.
The drawback is that it will be slower than if you did this through Photoshop or another graphics editing program. The reason I needed Bridge to do this was because I have a sequence of processing for images when I do photos for a client. Extract jpg from CR2, copy jpgs to that users specific local folder, watermark them with a "PROOF" logo, upload them to their album on my website and, once they submit an order, get the order and label all the photos the client wants. This is all done in Bridge via javascript with only a few clicks on my part to set up for the specific client.
An option I used to use was to have Bridge create a .bat file then run it. The .bat file would run ImageMagick on the images and add the watermark. So that's another option, though it isn't specifically Bridge doing the watermarking. There is also a way to have Bridge "talk" to Photoshop and tell Photoshop to do certain tasks which could include watermarking images in batch.