Interesting question,. I've used Greek yogurt in the past as a marinade for chicken and lamb with good results, but never thought about doing so with a brisket. That said, I don't see any reason why it wouldn't work with brisket.
If I were in your position, and interested in trying the yogurt marinade, I'd cut the brisket in half, coat one half with the marinade, leave the other half bare, and cook them as you normally would. Use full-fat true Greek yogurt, preferably made from goat's milk, if it's available, and strain it well. Mix in any seasonings that you might normally use, coat one of the brisket halves with the yogurt, and refrigerate for at least 24 hours. Cook the brisket halves side by side, and go from there. If you choose to try this, let us know how it works out.
Nothing ventured, nothing gained.