I can only say for sure for Mario Kart 64. If you read the description before you download it, it says that due to technical difficulties, you cant save ghost data and that Nintendo are sorry for the inconvenience. I have been able to save Mario 64 and if you go back to wii menu from using the home buttom from super mario bros it should stay where you left it when you restart the game. I'm just going to check these for you now. I will edit when i'm done.
mario 64 saves in-game and super mario bros will let you use the home button to go back to the channels and then when you restart the game you will be wherever you pressed the home button just as i said.
Hope this helps.