Many things are possible given enough time, money, mechanical aptitude and proper tools. Whether something is worth doing is another story.

If you google "derailleur hanger for horizontal dropout" or "derailleur hanger for track bike" you'll find some things made specifically for your situation. They look similar to the piece you showed, but they're a little different.

I'm assuming you know you can't use your current hub with a derailleur, so you'd need to replace the rear wheel entirely, or lace in a different hub.

Definitely a lot less hassle to find a frame/bike built for a rear derailleur than to try to adapt a rear-facing dropout on a Pashley.