I've done this with a version I compiled myself to allow save states online, as well as older versions from before it was disabled. I have successfully stayed in sync by pausing Dolphin, as the host, and then the other player loads the state before I also load the state and unpause it. Because loading states online can work this way, I think it would be better if the host has the option to allow save states to load online when starting the netplay game, perhaps with some type of warning. That said, the type of state loading I was doing isn't really suited for a TAS, but a replay of regular gameplay would probably be ok.
Edit: I believe the method I mentioned had problems with Wii remotes. Using boot to pause in debug mode and loading the state while the game is paused is the most reliable.
Edit: I believe the method I mentioned had problems with Wii remotes. Using boot to pause in debug mode and loading the state while the game is paused is the most reliable.