If they can get back this far (466BC), with some careful calculations and a bit of luck, they should be able to go back further. They just need to look in those records which have been kept and see if anything coincides.
You have all the possible gravitational perturbations to take into account in the comet's orbit, over time. Makes for some hairy calculations!!!. You can never pin the orbit down with any certainty.
Not just gravitational perturbations, you also have non-gravitational perturbations which contribute to a comet's orbital prediction.
It is quite fascinating to dig in the past to find these writings, you'll be quite surprised to know that the Chinese and Arabs kept very good documents relating to celestial events, although i'm not sure what the Australian aboriginals made of comets and i am curious to know!