There are no reliable contemporary depictions of Charles (his seals show him with hair), so we don't really have any idea. It's been suggested that his nickname might have been ironic, the way you call a fat guy "Little Charles", but there's no real proof either way.

Being bald is in fact not always a total negative. For example, it's a common rumor that the Julian dynasty of Roman emperors was sequentially bald then hairy, a sequence which has repeated in Russian leaders since 1825. Who knows, if the Carolingians had heard the rumors of the Julians, they might have thought it an important part of their claim to be Holy Roman Emperors.

Paul Dutton’s fascinating chapter on the symbolism of hair for Carolingians, “Charlemagne’s Moustache” (in the 2004 book by the same name) speaks specifically to your question (pp. 36-38) and concludes that for now it is unsolvable:

Was Charles in fact bald? His crown-covered head in the surviving illuminations disguises what was there or not there. The king’s pate on the [equestrian statuette] (http://www.louvre.fr/en/oeuvre-notices/equestrian-statuette-charlemagne-or-charles-bald) [traditionally Charlemagne but now believed by many to be his his grandson Charles] does possess a clear design of hair and below the crown a full fringe of short hair that surrounds the back of the rider’s neck but never touches his shoulders. . . . And Janet Nelson and others have suggested that the epithet may be ironical, that in fact Charles, the grandson of Charlemagne, may have been extremely hairy. If that were true, it would be exceedingly strange that no one from Charles’s chirpy court ever commented on his hairiness. And, indeed, the so-called Genealogy of Frankish Kings, a text that comes from Fontanell perhaps as early as 869, does explicitly state that Louis was the father and Judith the mother of “Karolus calvus” [bald] and it is a source without a trace of irony. By the end of the tenth century, Richer of Rheims and his near contemporary Adhemar of Chabannes would both call Charles “the Bald,” but only that one Carolingian source seems to talk about Charles’s hair and it is unlikely that it was the source of the later use of the epithet. If Charles’s baldness was ironical and he was, in fact, a strikingly hairy Carolingian, why do we not find even one Carolingian poet making sport of the comic imagery of it all? If he was actually bald, why did disapproving enemies such as the east Frankinsh annalists ignore the epithet entirely? Instead, they preferred to call him a tyrant, but why would they have missed the opportunity? In any event, the Carolingians seemed to have largely ceased thinking that hair was a source of powerful symbolic importance. We may never know whether Charles II was bald . . . .