Nope you'll have to re-buy it from the Wii Shop Channel
I have the limited edition red 25th Anniversary Wii with Super Mario All-Stars pre-installed as a channel. I reformatted the Wii to get rid of all the Mii's and save files, but it deleted the pre-installed All Stars game as well.
Can I get it back?
If the all-stars game are in the Wii-Shop, can you tell me what to search for, because I can't find it with "Mario", "Super" or "Stars".
All 4 of the games are there individually, but only as NES emulators. The games in 25th anniversary version have cleaner graphics and are a bit nicer.
I'd imagine that if ya can't get that Anniversary Super Mario All-Stars pre-installed junk back via Wii Shop, you'd have to contact Nintendo directly. Go here, select your country, grab Nintendo's contact info (at the bottom of the page) and get in touch with 'em to see if there's a way for them to get you back your stuff.