Even the great Charlie Feathers said:
And drums don't really work with rockabilly. They collide with the bass. It isn't really rockabilly if you use drums. That turns it into just rock. Well, drums are OK on rockabilly if it's just a running lick, like Buddy Holly's 'Peggie Sue' - that's rockabilly, when you keep that flow going. That's what Scotty Moore (sic) and them gave Elvis. But if it's laid-down, straight backbeat, like Carl Perkins had, that isn't rockabilly. Half the drummers don't know how to drum, to start with. They're timekeepers, that's all they are, with no dynamics. And dynamics, that's part of the show in rockabilly. That is exactly what it's all about, right there.
But check out the drumming of D. J. Fontana on Elvis' 'My Baby Left |Me'- sublime. Gene Vincent and His Blue Caps, Carl Perkins, The Rock n Roll Trio (on record at least,The Rock n Roll Trio used session drummers for recordings) all featured drummers.
W.S Holland was Johnny Cash's drummer for about a million years. His illustrious career started out with Carl Perkins in a most unusual manner. Holland would beat out a rhythm on the body of Jay Perkins' bass:
"On a Saturday night, Carl said, 'We've got an audition at Sun Records next week,'" Holland remembered. "'Get some drums and go with us.' I told him I'd never played drums, but I borrowed a set the next day. I set them up backwards, because I didn't know the difference. Tuesday, I went and played with them at the Cotton Boll. Thursday morning, we went to Memphis...On the way back to Jackson, we were all laughing about it," Holland said. "I mean, the second time I ever sat on a drum stool in my life, I played on a record."
In Gene Vincent's 'Be-Bop-A-Lula,' an undeniable rockabilly classic, Vincent's Blue Cap drummer Dickie Harrell demonstrated that it wasn't necessarily the volume of the beat that made it work, but the manner in which it was delivered. In 'Be-Bop-A-Lula,' a Top 10 hit in 1956, Harrell used brushes instead of drumsticks and created a sexy, circular snare drum rhythm. He moved the song along with innuendo and cool dynamics. A very hip drum part, it's a perfect example of the way restraint in drumming can give the music momentum and power.
Max Weinberg - Let There Be Drums sleeve notes.