Extrinsic motivation is not necessarily more motivating in the long run, nor should it be, but it is a great lead into having a student become more motivated. Let's say you have a student with a "I can't do" attitude. Initially, to get them over this hump, extrinsic rewards are great. But, then as the student becomes more proficient, s/he no longer needs the extrinsic rewards because s/he will automatically start intrinsically rewarding herself/himself with each success.
On the flip of this however, one could argue that extrinsic rewards are the most motivating. Most people work because of extrinsic rewards re: money, benefits, etc. When my son was in high school I paid him for each A & B he achieved on his report card. Why? Because this was his "pay" for his work. It was extremely motivating and he graduated in the top 10 of his class.
So, the answer is, sometimes yes and sometimes no. It depends on just how much the student needs to be motivated. In my son's case it was the motivation to get him from "I can't" to "i can".