Certainly. And the process is the same whether you're doing it in Premiere Elements or CS5.
You just place the watermark graphic on an upper video track, extend it for the length of your movie and size it as necessary.
There are just two things to note:
1) This will require re-rendering your entire movie, since the graphic changes every single frame of video.
2) If your graphic is square, it's just like creating a picture-in-picture. However, if your graphic is non-square or irregularly shaped, you will need to create a graphic with an alpha channel rather than a background layer. (I explain how to do this in detail in my combined Photoshop Elements/Premiere Elements books, available on Amazon.)
The basic principle is that you open the graphic in Photoshop Elements and double-click on the background in the Layers palette so that it becomes a floating layer. Then you delete any of the background you don't want to show up in Premiere Elements and save the file as a layered PSD.
Along with Steve's instructions, you can also adjust the Fixed Effect>Opacity, for the watermark Clip, to make it more subtle. If the watermark is not Scaled, or positioned, exactly as you would like, you can also use the Fixed Effects>Motion>Scale and Motion>Position to make those adjustments.
To adjust those Fixed Effects, you would Select the Clip of the watermark, to to the Effects Tab, and then Edit Effects to access the Effects Control Panel. There, you will find Opacity and Motion (which, when twirled open, will reveal both Scale and Position.
PS - one can do this in Titler too, and the operations will be the same.