No, no...no. Don't do that. It's an old wive's tale. It's what Tom alluded to - liquid causes a fish's blood to clot. Sorry, but Sprite, Coke, Mountain Dew, etc. do not contain magic elixirs that miraculously stop bleeding. The fact that they're not for consumption by animals leads me to believe they're more harmful than good.
Instead, place the bleeding fish in the livewell and add "Please Release Me" formula. It not only stops bleeding, but provides vital medicine that gives the fish a better chance of survival.