I am fairly certain that it is impossible to actually finishing a LARGE lollipop without biting. At least, I do not have the courage to endure such a task. I once licked a flavorful pop to the point where I could feel the awesomeness of the sweet bubble gum in side, but then my emotions got the best of me and I gave it to the bite.
I just found this little gem online though, "A group of engineering students from Purdue University reported that its licking machine, modeled after a human tongue, took an average of 364 licks to get to the center of a Tootsie Pop. Twenty of the group's volunteers assumed the licking challenge-unassisted by machinery-and averaged 252 licks each to the center."
So there you have it.