No, for two reasons.
First, Obama's only half-Kenyan on his father's side, and has never lived there himself (he was raised partly in Hawaii, partly in Indonesia). His father was hardly even a factor in his life. Even if he were 100% Kenyan, he wouldn't have been the first of that nation to have received the award. Wangari Maathai - a Kenyan environmentalist and political activist - won the prize in 2004 for "her contribution to sustainable development, democracy and peace."