C. Kirabo Jackson has a new study and his conclusion is a qualified yes:
…the incentives produce meaningful increases in participation in the AP program and improvements in other critical education outcomes. Establishment of APIP results in a 30 percent increase in the number of students scoring above 1100 on the SAT or above 24 on the ACT, and an 8 percent increase in the number of students at a high school who enroll in a college or university in Texas. My evidence suggests that these outcomes are likely the result of stronger encouragement from teachers and guidance counselors to enroll in AP courses, better information provided to students, and changes in teacher and peer norms. The program is not associated with improved high school graduation rates or increases in the number of students taking college entrance exams, suggesting that the APIP improves the outcomes of high-achieving students rather than those students who may not have graduated from high school or even applied to college. Nonetheless, APIP may be an exceptionally good investment. The average per-student cost of the program, between
$100 and $300, is very small relative to reasonable estimates of the lifetime benefits of attending and succeeding in college.
Here is a recent article on the topic. My intuition is that this works best for unmotivated students, where there is no intrinsic motivation to undermine.