As Shonumi suggested, local play would be the easiest thing to do. Still, I have played Mario Party 9 online and it does work. It is very important that certain settings are exactly the same for everyone. For example, if someone has a nunchuk turned on for Wii remote 1, but another person doesn't, that would cause a desync. There are other settings such as cheats, which also need to be the same for everyone.
If everyone is using the exact same version of Dolphin with the same settings, I would see no reason why it shouldn't work. Also, I'm assuming this is a recent build of Dolphin, since older ones could have more problems.
If everyone is using the exact same version of Dolphin with the same settings, I would see no reason why it shouldn't work. Also, I'm assuming this is a recent build of Dolphin, since older ones could have more problems.