The question is complicated, because the study of genealogy has elements that resemble science, but it also has elements that resemble art. In this sense, I would say that it is not a "true" science, but it has elements of science. Let me explain.
When studying genealogies, you are mainly dealing with evidence and data. On account of this, it is scientific, because you cannot do away with the evidence; in other words, you are circumscribed by the data. Moreover, other scholars can look at your work to recheck your conclusions. This, too, makes it scientific.
With this said, often the data is incomplete. For this reason, scholars have to make conjectures. This is where creativity comes in, which makes it artistic.
In the end, the study of genealogy is both scientific and artistic.