In more precise terms the question can be interpreted as: whether realistic probabilistic models of evolution are identifiable, and/or whether particular reconstruction procedures are statistically consistent. That is, can the model with all its parameters (such as the topology of the genealogical tree, the lengths of all the tree branches, or various rates of mutation) be inferred given unlimited amounts of observable data.
In any evolutionary process a lot of information is lost over time but it might still be possible to reconstruct some of the structure, such as the evolutionary tree but not the exact DNA profile of all the ancestors, from complete data on the living descendants. Whether a single tree can be consistently assigned to the set of DNA samples is dependent on the reconstruction procedure, and different procedures will arrive at different trees.
http://arxiv.org/abs/0912.0041
http://arxiv.org/abs/0808.2660
http://arxiv.org/abs/0708.2124