So, it sounds like you are under this Edward Pool of Rowan County, and trying to connect your tree farther up? All three of the Pools you mentioned would be about 4 generations after Robert, so I am guessing you still have a ways to go.I do agree with you though, with Robert the father and John the brother dead and neither with any other offspring or family to inherit their property, it would seem most likely that all the Pool/e's in this area decended thru Robert.
My "smart match" function in "myheritage.com" site found someone else with Robert Pool in their tree, and with a son named Richard Poole 1625-1674 (listed in his tree as born in England and died in Virginia, seems incorrect due to the fact that we know Robert was already in Virginia). This is the only Pool info I see in this persons tree, it appears he is tracing a different family name. The Richard Poole in his list was married to Mary Ward born 1635 in Virginia and died at unknown time.
Maybe little by little additional offspring of Robert will be found.