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I'm having a slow day at work (waiting for renders) so I've done some maths!
My guess was pretty close as an orbit with a semi-major axis of about 42500kms (apoapsis of about 84500kms) would have a period of around 24hrs. From this I figure that an observer at the equator would see the satellite, at apoapsis, about 4.5 degrees from the SCP. This error would decrease as one got closer to the south pole. At around the latitude of Sydney I figure the error would be a bit over 2 degrees, still too high to use for alignment given Polaris's separation from the NCP is only about 0.7 degrees (I think).
Perhaps you could have 10 satellites in 10 day orbits so that one is visible at the SCP at a certain time of each night, this might reduce the error enough to make it useful, except that everyone would have to align at the same time or they miss out for that night!
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