AQ would consider this excellent news. Millions of young Egyptian men, all muslims of course, will be angry at the USA and will sign up en masse as suicide bombers, foot soldiers, and every other kind of AQ helpers.
Hurting them in the wallet works only with economy-oriented societies, such as democracies (who rise and fall on news from stock exchanges) and dictatorships (who always complain that the last palace is not fully gilded yet.)
A theocracy of 6th century does not want money. Furthermore, money is dangerous to it because it separates people into classes and creates private interests. Egyptian computer scientists would want different things than egyptian goat herders. Fundamentalists want everyone to be illiterate goat herders; the only skill worth having is how to make IEDs. This is exactly why Communists were killing educated people in Russia, in China, in Cambodia... they couldn't allow smart competition.
The fundamentalist crap you refer to is for the PEOPLE, not the ruling class. The Nazis, the Commies, the aristocrats of pre-modern Europe, & every other potentate have been feeding the “stupid” class this stuff since government was invented.
It is ALWAYS about the money & power for those asking OTHERS to sacrifice everything.
Egypt is no Afghanistan. People have A/C, TV, cars, cell phones, clothes & cash to spend. Take that away & their society will collapse. Egypt is definitely a economy oriented society & that economy is hurting as a result of the radicals. I expect a backlash.
In a world war on multiple fronts with multiple enemies, attacking one enemy often satisfies another. Al-Qaeda has no love of Egypt. It is the enemy until radical islam takes over. From their perspective, chaos in Egypt is good until they take over. Anything that Israel does that weakens Egypt makes the takeover that much easier. If Israel avoids war because it might strengthen AQ, then it can simply wait to be destroyed.
Furthermore, AQ is a far less dangerous enemy that Egypt. AQ has no air force, navy, or army - Egypt does. Far more people have been killed in Israeli/Egypt wars that ALL the deaths caused by AQ.
There is not much Israel can do to stop a radical islam takeover in Egypt, but it can destroy the Egyptian economy with a few missiles or bombs; & the Egyptian military knows it. Without the economy to sustain the military, it rots, quickly. I doubt AQ cares, but Egyptians do.
As for million of radicalized Egyptians, they are just cheap cannon fodder for the Israelis. I've heard that threat many times & it just doesn't cause anybody any concern. Truth is, most muslim terrorists are cowardly thugs who run like rats when confronted.