There are examples of feudal armies conquering large parts of land (e.g., Philip Augustus taking most of John's continental possessions). It took quite a while to reduce all those castles, but it was possible. /QUOTE]
Well, Philip Augustus was dealing with a purely feudal opponent who was not even excessively active and did not necessarily have a strong support in the region. OTOH, in the Northern Italy the emperors had been facing a strong opposition of the rich cities of Lombardi and Tuscany. Situation somewhat similar to the fight of the (French supported) Counts of Flanders against their cities. Ghent was capable of standing up to the French (and count's) forces almost on its own for quite a while. In Italy the anti-imperial coalition was, seemingly, even stronger (or the imperial forces weaker?).
The castles were bad but taking a well-fortified reasonably big city supported by its neighbors was a completely different kettle of fish: unlike the castles, they routinely had enough armed people to kick at the besieging army with a noticeable success (as happened to Barbarossa at Legnano and to the troops of Frederic II at Parma).
I don't think pikes would be necessary, though; siege warfare was the main reason why conquering things was so hard, so you'd be better off having a professional siege train.
The pikes would be (anachronistic but) helpful because the HRE armies had been cavalry-heavy while the armies of the Lombard League had considerable numbers of the foot soldiers (at Legnano they hold front allowing the League's cavalry deliver a final attack on the flank).
Not automatically, but it does help. As for getting the nobles on-side, the traditional way was to give them estates in the areas you conquered, and since Italy was pretty wealthy, that could provide a way of getting people to join you.
But the wealth was in the cities which were mostly against the emperor. The problem with an exclusive reliance upon the nobles was that, after they got their estates, etc. they had little incentive to keep fighting. And the things like discipline and complicated tactics simply did not apply. Even the discipline on a battlefield is something that happens to other people (like at Battle of Tagliacozzo where Conradin's knights started looting before the battle was over). OTOH, the mercenaries would be loyal as long as you are paying (and if you are lucky, even beyond that if there is a loot) and you can introduce at least some drill.