Hum, yes, because that which is humdrum has the monotony of the humming of a bee or other insect.
But drum, well, did this added syllable, back in the sixteenth century, also convey the monotone of a drumbeat?
It is doubtful, though such could have been the case.
But it is more likely that drum was added merely because it rhymed with hum and just happened to be a word itself.
