Does being an underdog make you more motivated than the competition?

No.

Via Your Pinkie Is More Powerful Than Your Thumb: And 333 Other Surprising Facts That Will Make You Wealthier, Healthier and Smarter Than Everyone Else:

The favorites, it turns out, try 30 percent harder when they face underdogs, a new study shows. Favorites try harder because they have more to lose, and they fear the humiliation of losing to teams they should beat. The results of the study contradict the common belief that underdogs have more motivation than their competition, and the researchers say this applies far beyond sports. In fact, they arrived at their conclusion by administering a series of tests to college students. In one test, students were asked to do an incredibly mundane task: cross out vowels on documents. The students were competing against students from other colleges, and they always knew the identity of their competition. That information caused students from more academically prestigious colleges to try harder than groups of students that didn’t know against whom they were competing.