Based on the overall span, I don't see how 3 sections would do it and not being overly bouncy, and eventually sagging over time. I suppose, if you did it as you say, using overly long spans, and you concluded that it was not supported well enough, you could always go back and add more supports.
I am also cautious to agree with your idea to use a power auger to drive the posts knowing that at some point the points are sure to grab. I subscribe to the K.I.S.S. methodology; just spin them in by hand first and see how that goes before making the task more complicated than it may require.
