It is possible, but would take some work. (I have not tried this, so it may not be 100% accurate.)
You would need to have the global watermarking options turned off (no watermark). Then you would need to create a plugin that attached to the new_image filter. That filter would call the cacheImage function with the appropriate parameters to cause it to create the cached image including a watermark.
Of course, if you do this and purge your cache, all those watermarks will go away.