Is it true that Occitan & Catalan together are more mutually intelligible with Italian than is Spanish despite the last sharing a degree of communicability with Italian?
Yes. Because of the way that the language continuum works, Catalan and Occitan are closer to Italian. Our grammar, vocabulary and some sounds are very similar to Italian, more than Spanish is.
However, Italians can have difficulty understanding the accent of Eastern Catalan and most of Occitan, because of the vowels like ə that Catalan and Occitan have but Italian and Spanish don't. For this reason, if they're not used to hearing our language/identifying our sounds, it can be easier for Italian speakers to understand Spanish. But written down, Italian is generally closer to Catalan and Occitan than to Spanish.
Still on vowels, on the other hand, Catalan and Occitan differentiate open and closed E and O (è, é, ò, ó) same way Italian does, but Spanish only has the closed ones. Other sounds like g (as in giraffe), z and sh (spelled ix in Catalan and sc in Italian) are also shared, while Spanish doesn't have any of the three (in their place, Spanish has the hard j and th that neither Catalan nor Italian have, and ch which all three have, respectively). So you see, it has differences but also many similarities.
Italians should have an easier time understanding Western Catalan accents. In fact, historically it has been considered that Valencian (one of the accents of Western Catalan) is the "central" or "bridge" Romance language that can be easier for the others to understand.
