Somehow I’d missed this one, though I’d seen people toss the name around (and assumed they were joking). But it seems that yes, the Legion of Super-Heroes did in fact once reject Arm Fall-Off Boy:
Legion of Super-Heroes in the 31st Century #16, out next week.
Arm-Fall-Off Boy first appeared in an issue of Secret Origins, in which we saw the secret origin of the Legion Clubhouse. Needless to say, he was rejected.
He next appeared in the Post-Zero Hour continuity as “Splitter”, but fared just as poorly.
Now we have the third version, from the animated show continuity (the picture you have above).
You’d think he’d make an excellent distraction. Especially when a villain gets to monologuing.
From what I hear, he saves the day…one-handed.