I know John Bonham only from my very limited exposure to his playing on Led Zeppelin albums. I heard their debut when it came out, and found it unintentionally and almost hysterically funny, like the bar band in the movie Ghost World: Blues Hammer. The name is quite apropos, as that fake-Blues band heavy-handedly bludgeons the music to death, employing no restraint or subtlety what-so-ever. As did, imo, Led Zeppelin. And in anticipation of the possible reaction to this statement by some readers: no, I am not saying this thinking it makes me sound cool (or whatever).
But by the time Led Zeppelin I came out, I was already listening to the Blues Levon Helm had grown up listening to and then playing in The Hawks, that of it’s originators: Muddy Waters, Howlin’ Wolf, Big Joe Turner, Little Walter, Sonny Boy Williamson, Robert Johnson, Freddie and Albert King, Slim Harpo, Roy Brown, Wynonie Harris, Jimmy Reed, etc. As well as the American bands that had been putting out albums of Chicago-style Blues for several years before LZ showed up: The Paul Butterfield Blues Band---whose black rhythm section Paul hired away from Howlin’ Wolf---and Charlie Musselwhite primarily.
That may not be enough to determine if Bonham could have played in The Band, but imo his bass drum technique alone would have disqualified him. Like many Rock drummers, Bonham "buried the beater." That’s what drummers call punching the felt beater of the bass drum pedal into the batter head and leaving it there, rather than letting the beater rebound off the head, which is called "feathering." Burying the beater causes the forward momentum of the music to stop and start on every down beat (the 1 and 3 in 4/4 time). I can’t get past that in the music of LZ.
Levon Helm employed feathering (as do jazz drummers), and other subtle aspects of the approach to playing the drumset (Buddy Rich "approved" of Levon’s playing 😉). Bonham may have had his strengths, but subtlety was not amongst them. Levon was also very sparing and selective in his use of the crash cymbal, a rarity in Rock music. Most Rock drummers tend to crash at the end of every measure (4 beats in 4/4 time), for no musical reason. Such cymbal crashes chop the music into separate little sections, rather than one forward-moving train. Bonham was very guilty of that musical "crime". He didn’t know which notes to leave out, overplaying---again, very common amongst the drummers in Rock bands. The Band were not a Rock band, they were a Rock ’n’ Roll band.
To hear how "sluggish" Bohham’s drumming is, listen to his opening in the LZ song "Rock ’n’ Roll", and compare it to the "crisp" drumming of Earl Palmer on Little Richard’s "Keep A-Knockin’", which is from where Bonham "borrowed" his part.