I've actually read about that, IIRC there were something like 18 different languages in the unit, which IIRC was a company, not a regiment. So the only common language everyone had some experience with was English, but that was a bizarre circumstance.
If this is anything beyond a myth it would be a rare exception. Each regiment recruited its men from a distinct province so at least the men would speak the same language and same province regiments were usually paired in Brigades. The command language in all non-Hungarian regiments was German, but a WWI army wasn't a place to study the finer tones of human communication. Soldiers were drilled to do this and that without giving it further thoughts or discussion and the command itself often wasn't recognisable in any civilian language. I can sure tell you as an example that the Danish command for "Present arms!" wouldn't be understood by any Danish speaker - it simply has been through too many mad drill sergeants. "But who cares, at this gutteral sound you just do this, and we train it until you can do it at sleep!"
Anyway most citizens in the Empire spoke and understood a little German - not enough to study litterature, but certainly enough to be drilled. BTW in WWI tens of thousands Danish speaking from Slesvig/Sønderjylland fought in the German army (and 5300 fell) - I have not seen one remark about the German command language being the problem - I'm sure a lot of other things appeared much more problematic.
Our current view on the KuK is very much seen through its successors who had to legitemise themselves by saying: "Look people, we just saved you from something absolutely hopeless and rediculous - how lucky you are!" Not just the politicians but also in litterature, like in the (unfinished) novel "The Brave Soldier Schwejk" by the Czech writer Jaroslav Hasek. It is actually a very well written story, and quite funny, but was as much a showdown with militarism as with the KuK. As pacifism was quite popular among intellectuals after WWI the novel became very popular (a TV series was made in the 70s), also because you through it could critisise militarism without being too hard on your own nation. The KuK had none to defend it after 1918 but was quite handy as a scapegoat.
From my own contact to not at least Poles it is my impression however, that there has since been a growing recognition of the KuK. I have even heard Poles, who lived before 1918, say that Poles never had a better time than during the KuK!
What first of all tied the KuK together was the Emperor and the army, and with the last gone the rest went too. By early 20th century the Empire sure was challenged by modern times, who wasn't? National identity is usually seen as the main challenge to the KuK, but actually I have come to doubt about that. By WWI national identity had been "modern" for a century but what IMHO was the problem was the too dominant place Hungarian national identity had been given after 1867 - it was that and not the inherent idea of the Empire that stopped room being given to other (Slavic) national identities.
The (Habsburg) Empire is often in general being seen as a colossus on clay feet - but actually it had a major position in Europe for longer than anyone else since the Roman Empire - not much clay feet in that! *
*) I count from 1439 after which Habsburg occupied the Emperor title until 1806 and after that also had the major position until at least mid 19th century, and a great power status until 1918. But already Rudolf I in 1273 was the first Habsburg with a major role.