This could be something you can theoretically script and bind to a hotkey if I’m not mistaken (@Ofnuts does something like this already exist?).
Probably:
- Open (as a layer) a PNG saved on your machine somewhere.
- Move to the top of the layer stack.
- Make active (so you can immediately move it around, rotate, whatever).
Then it should just be a keystroke to invoke the script and automatically place your signature.
Also, if you save your signature/watermark as a transparent PNG file somewhere, you can also just drag and drop it over your canvas in GIMP.
You could even got a step further and save a couple of different versions of your watermark, normal and rotate 90° in both directions - then just choose the one you want.
[edit] - there’s also a thread here where we looked at doing this bulk with imagemagick - so if you wanted to automate it further you could possibly try on of these: