Would the western Romance languages be intelligible if the Carolingian realm never split?

Let's say Louis the Pious lives longer and the Carolingian empire stays united until at least the 1600s, with territory including modern France, Lombardy, and Catalonia at the very least.

Would this prevent French, Italian, Occitan, and Catalan from diverging? I've seen it written that 11th century Oïl, Oc, and Si languages were much more intelligible than today, with mostly vocabulary differences dividing them (with even these being very localised, differing even between towns/cities). Would a single realm be enough to pin down the language to a single standard, or would/could they still diverge?

Would someone need to drastically centralise the state as France did historically (this did not exactly help France assimilate Occitan or Provençal) or would a loose amalgamation be enough to later standardise through the printing press (like the HRE with Luther's standard German)?

Also: what would the administrative language of Carolingia be? Would it be much closer to Ecclesiastical Latin, or still develop like French?
 
Considering how linguistically diverse France was IOTL, I can only assume that Carolingia would be at least as diverse as that, and probably more so. (Let's ignore the Germanic, Slavic and Celtic parts of Carolingia for this purpose.)

The combination of distance, slow travel, lack of mass literacy and minimal centralisation would still be issues.

Assuming Carolingia doesn't expand, and maintains its OTL pre-Treaty of Verdun borders all the way to the present day, you still have Iberia, and southern Italy. From what I have read, Iberian Romance, Italo-Dalmatian and Gallo-Romance had already diverged from Western Romance by the time the Carolingians rolled around.

However, there's no guarantee that Carolingia doesn't manage to get a dominant language. Similarly, there's no guarantee that the languages diverge in the same way.

Language standardisation typically involves - (1) printing [and, by extension, dictionaries], and (2) mass literacy, via compulsory education.

Could there be some kind of Standard Carolingian as a result of this? Sure, why not. IIRC, Standard Dutch was formed by a combination of words from multiple Dutch dialects. There's no reason why something similar couldn't be applied here.

However, there is still the issue of who runs the education establishments? If they are run on a regional basis, or there is a strong enough regional language already in place, it's possible that there ends up being multiple standard languages (e.g. one for each Duchy) - French, Aquitanian, Burgundian, Lombardian etc. - with no one dominant language.

Not that people haven't tried constructed languages...Esperanto, anyone? :p

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As to the administrative language, it would probably be Medieval Latin for a long time, since every educated and literate person in Carolingia would learn it. There's a reason why Latin was used as an administrative language in the Habsburg domains for ages - it was a neutral common language, which was not the native language of any ethnic group.
 
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