Personally, I think smart kids can follow Calc without too much trouble since all you need to do is to follow the instructor and do you HW. If you do enough problems, you will get it. For AMC and AIME tests, on the other hand, there are always problems that one needs to be creative to solve them. My son is smart but not exactly a genius. He worked on all old AMC examples and still could only barely make it 120 in AMC 10. For AMC 10 and 12, you certainly need a lot of exercise, unless you are a genius. But to be creative and have some talents is necessary in my opinion. To do well in Calc, however, requies only hard-work for mildly smart kids.
My two cents.
My two cents.