The 'Italian' Frederick was an infant, if Philip survives and manages to position himself in the Empire, then the Princes of the Empire (Reichsfürsten is less cumbersome term) will prefer to follow the German Philip over the Italian Frederick. Furthermore Philip will have the Papacy on his side for a change.
No matter how rich Sicily was, it couldn't take on the Empire, if the Empire would unite. Philip getting a Papal blessing, would be enough to unite enough Guelphs and Ghibellines.
Frederick was hardly likely to remain a child all his life and your argument previously seems to be predicated on the idea that at some stage, Frederick will be in a position to assert himself. Otherwise Philip would not need to persuade frederick to remain just King of Sicily
Your faith in the princes of the empire lining up behind Phillip, seems somewhat mystifying, given that in OTL the princes were fickle likely to change their alliances quite regularly and for personal gain. Most of those Princes were raised in an environment of Primogeniture and I'm not as convinced as you seem to be, that they would readily support the division of their lands among their children.
The Guelphs and the Ghiberlines although nominally split into pro papal and pro emperor factions were in fact often motivated by quite different aims.
The Popes found out with Otto IV, and with other monarchs, that election to Imperial office was more than enough to spark an interest in uniting Italy under their control. Maybe Philip would have been different, but I doubt it.
No Hohenstaufen actually seems to have allowed his actions to be dictated by the lack of support of the Popes, and unless hearing of Papal support made Philip die from shock, I doubt that Papal support would have an impact this time. But for the record, the Pope consented to the election of Frederick as King of the Romans and Emperor Elect after Otto IV invaded Italy and asserted his Imperial rights, and so there is no reason to think that any invasion of Italy by Philip would lead to a different Papal response.