In truth there is not a lot of research about the effectiveness of sponsorship. In the following article Bruce Wydick and company attempt to gather that research and found some very positive outcomes for sponsored children versus their non sponsored peers.

From “Chicago Journals” (April 2013) an article titled “Does International Child Sponsorship Work? A Six-Country Study of Outcomes” By Bruce Wydick, Paul Glesse, and Laine Rutledge.

Article abstract:
Child sponsorship is a leading form of direct aid from wealthy country households to children in developing countries. Over 9 million children are supported through international sponsorship organizations.
Using data from six countries, we estimate impacts on several outcomes from sponsorship through Compassion International, a leading child sponsorship organization. To identify program effects, we utilize an age eligibility rule implemented when programs began in new villages. We
find large, statistically significant impacts on years of schooling; primary, secondary, and tertiary school completion; and the probability and quality of employment. Early evidence suggests that these impacts
are due, in part, to increases in children’s aspirations.

Full article can be found here:
http://www.jstor.org/stable/pdfplus/10.1086/670138.pdf?acceptTC=true