Interestingly, the game starts just fine! I expected to see the same "insert disc" error that SSBB NTSC gives.
Unfortunately, only the bootloader runs. The trilogy loads a boot menu of sorts that plays an intro video, allows you to pick a Mii (to represent your savegame), and allows you to choose your game and the game's difficulty (normal or veteran).
Before choosing the game, however, the game will attempt to connect via WiiConnect24. Just wait until it times out and continue.
I've noticed on my Wii that the Wiimote disconnects and then reconnects after I have picked the game I want to play. This suggests that the loader points to the appropriate gameboot. I suppose this is why Dolphin cannot continue as loading another gameboot is probably not supported at the moment. You just end up with a black screen and frames no longer being rendered.