Yes, genome sequencing is one of the least subjective means used to infer common descent. It is still to some degree subjective, because we target specific parts of the genome that we think are useful - e.g. either conserved or variable across species.
It is impossible to say how accurate this method is, because we do not know the truth. We have no reference value. It is impossible to determine (i.e. prove) the relationship between species unless we observe the speciation; we can merely collect evidence that supports or refutes a theory of common descent.
There is a fairly comprehensive page on Wikipedia that describes the various types of Evidence of common descent.