No, I'm afraid not.
Although I'm sure the site is well intentioned and benefits many - there's no vetting done.
If I read it correctly, people simply create a profile and list their "wishes" - anything from Christmas tree ornaments to funds for surgery. That's a pretty wide scope of needs. And there's no way to tell if the needs are "real". The entire profile could simply be a scam, as is always the problem on the Internet. I also don't see how anyone donating could declare it as a tax deduction.
Social networking and collaboration is the next big wave of Web 2.0, so on a personal level, people may be interested in registered and exploring the site and selecting someone to hep.
However at the organizational level, if one of my organizations (PTO, work, school) adopted a family, it would work with a local 501(c)(3) or government entity or school officials - but definitely someone within our community.
If it were a registry of some sort, credibility would be important - knowing the stories are true, and ideally having your donation be tax deductable. For example,
The Children's Organ Transplant Association
(COTA) is one I support. It's 501c3 and also affiliated with United Way. For COTA, the cases listed are fully vetted, the donation process is managed, and if a child is lost before the funds are used, the funds are reallocated.
I know this a different scenario than Wish Upon a Hero, which is more an informal matching of needs rather than being an intermediary. But our organization would want the more formal scenario.
Good Luck.