Well if we found current or fossil life with a common ancestor on other bodies it would certainly demonstrate that it arrived via debris; whereas if we find life with no common ancestor or find no evidence of life at all that would reject the hypothesis. It wouldn't necessarily answer which body was the original birthplace, but for the purposes of modelling, whether life happened to start here is a much less impactful question than whether life had to start here. If all life here started here, then life had to develop quickly; if we could potentially descend from stuff in the pre-solar system debris field that could add billions of years to the clock, and makes interstellar panspermia highly plausible.