There are many attributes of the Church of which unity is one. As you have noted geographic division is another undeniable attribute. It is absurd to apply one attribute and make it the sole attribute of the Church. If unity were the only attribute then the Church would be the Borg, but it is not.
IMO it is absurd for me to think of unity to the point that I can summon St. Christopher to my side from heaven. The disembodied spirits of the saints are in heaven and their bodies remain here on earth until the resurrection. That is an undeniable division.
I have no means of knowing with any certainty (given my physical limitations) the present location of any disembodied saint, other than in heaven. As a result, I have no certainty that any saint is capable of hearing, much less interested in hearing, any prayers made to them. It is certain, from this discussion, that no saint answers the prayers in the form of acting on their own initiative and ability to cause the answer to come about, but that, at best, the prayer is transmitted to God for His answer.