A great idea!
I think the mentoring idea is much more feasable than a sponsorship.
Perhaps we need to set up a decent contacts forum as well, highlighting good practice and methods that have got people through the system. It would be difficult to prevent such a forum falling into the usual "this place is better than that" row, however.
And practical support for job hunting, CV writing, how to get yourself noticed etc.
I believe that would have a real value.