I started to wonder if it was possible to add a payload to a bitcoin
You can stop wondering. It isn't. You might just as well try to add a payload to a dollar being transfered via wire transfer for all the good it'd do you.
That said, bitcoin is very traceable, far less anonymous than cash. The fact that people think it's anonymous is proof that people don't really understand how it works. There are ways to anonymize it, but realistically I wouldn't trust any of them.