Some larger projects have what's called a feature bounty, like others have mentioned $20 is very low for someone not familiar with the codebase to do it, it might be enough for someone already familiar with it (but I seriously doubt it since it involves at least some refactoring of the UI to add a shuffle button). However if more people want that feature they can each contribute a small amount and eventually it would be a value that would justify someone to learn the codebase.
That being said, like someone else pointed out, it seems the app is going through some rewriting, so I wouldn't expect any new features (especially those involving UI) anytime soon.
Finally there are two issues mentioning shuffle in the GitHub, https://github.com/jarnedemeulemeester/findroid/issues/334 and https://github.com/jarnedemeulemeester/findroid/issues/547 you might want to create an account there and voice your wanting of that feature too, by either adding a thumbs up or a comment explaining why this is important to you.
Good luck, hope you get your shuffle play!
Edit: forgot to answer your question directly, yes, you can pay someone to contribute to an open source project, nothing wrong about that. But as a general rule it would be cheaper to give money to the people who are already working on the project.