EXCELLENT question.
No, I don't, and here's why:
They are the originators of rock music; they set the foundations for what would become "classic rock", but I don't think the pre-1964 rock is the same as "classic rock". These guys are, in the purest sense, the "oldies".
Rock music was a fad that came and went in the mid-to-late 1950s. It birthed a teen culture in the Anglosphere and was a big part of pop culture.
And then something happened by 1960: Rock pretty much died.
Many of the people you mentioned had either died, were disgraced or had retired:
Elvis Presley -- went into the Army in 1958 and retired from performing (for 10 years)
Buddy Holly -- died
Chuck Berry -- caught with a prostitute in 1959 and blacklisted
Jerry Lee Lewis -- married his 13-year-old cousin and blacklisted
Eddie Cochrane -- died
The fad of rock music had come and gone. There was a major lull between 1960 and 1964. .... Except in the UK where rock 'n' roll culture was still big and getting bigger.
Not only were British bands heavily influenced by the above-mentioned people, they were bringing those sounds into their own bands and some were melding it with something few Americans were doing -- Black blues music, like Howlin' Wolf, Muddy Waters, etc.
The Beatles basically jump-started rock 'n' roll outside of the UK and launched the British Invasion, and ripples that started from the British Invasion carried on, pretty much up to the present day.
So there were two early eras of rock music: the oldies era (1954-1960) and the classic rock era (1964-1977).