It is good that you have the correct genealogy before testing. It will be a lot more interesting. Most do not have the paper trails and go through the frustrating process of trying to reconstruct their genealogy with Y-DNA alone. The only success stories, besides answering specific questions, I know of involve a serendipitous match-up with someone who has a much older genealogy
Testing ascertains whether the purported relationships are plausible. It won't tell researchers how their ancestors are related. Only the paper trail can.
It is an excellent tool for preventing people from wasting time trying to connect orphan lines to unrelated families and identifying those family where documentary research might be fruitful.
The methodology was used in early studies at Brigham Young University. It involves testing known genealogies such as yours to validate them and to determine the progenitor's haplotype (the set of numerical results). If Rodney and Harry had matched exactly, their haplotype would have been the progenitor's haplotype, also called the family signature, ancestral haplotype, patriarchal haplotype, etc.
If they did not match exactly, but were close (41/43 or better) or in a gray area (39/43 or 40/43), it would be necessary to test descendants of other sons until there are matches on all markers. It is also possible to test branches of the first two to determine a mutation can be bypassed.
The next step is for those from orphan lines to look for a matching family. At BYU, this was actually done in two phases, but surname project now test everyone who wants to test. The ancestral haplotype is used for this and for matches between families because more recent mutations have be eliminated. This results in closer matches and clearer results.