They might, but there's no guarantee. Is Heinrich still King, and is he excommunicated/under realm duress. If the answer to either or both of the latter is yes, then you should see breakaways and rebel lords against him quite frequently.
The easiest way for you to expand is probably into North Africa. Just don't piss off Egypt and/or the Seljuk Turks before you feel confident about taking them on. Iberia is also a good option, and much richer than North Africa actually. Most, if not all, Muslim realms west of Egypt should definitely be manageable for you. When the time comes, Alexandria is one of the top-5 richest provinces in the game (Cordoba in Spain is in the top 10 too).
On the other hand, I recommend you try playing the dynasty game some too. When I recently came back to CK after a long absence and started with the Duchy of Aquitaine. After learning a few tricks (such as burning BB faster than in any other Paradox game by force-vassalising and recognising the claims of rebels, and gaining tens and hundreds of thousands of prestige when said rebels were claimants to conquered thrones), I achieved a WC after less than 200 years (=less than half of the games time span). The micromanagement after 5-10 kingdoms gets mind-blowingly tedious. I've now got an exceedingly strange new 'starting scenario': Europe is splintered, a true patchwork of tiny statelets, with the holders of some king-titles holding court far from the lands of their vassals, and the Mongols have just appeared in the east (hardly any heathen rulers left, though).
P.S. You mean Sicily. Naples is in EU I think? And in Vicky it's Two Sicilies. Confusing, eh?