Before you plunge in expecting a lot, my answer to the question in the headline is "I don't know."
The widespread reports last week of an "Israeli drone strike" against a jihadi site in Sinai, and claims by various jihadi groups operating in Sinai to the effect that the Egyptian and Israeli armies were cooperating in that operation, were swiftly and sharply (and predictably) denied by Egypt. In reading the denials, however, it is not entirely clear what is being denied: certainly Egypt says it is not coordinating with Israel, but is it also denying any Israeli involvement? Israelis are themselves well aware of the sensitivity of cooperating openly with Egypt, but have done so in the past, especially on issues involving Sinai and Gaza.
For a year, since a jihadi attack on Egyptian border guards, the Egyptian Army has stepped up its operations in Sinai, which had been neglected in the Mubarak years and which became a sanctuary for radical (and some criminal) elements after the 2011 revolution and opening of many prisons. But since the July 3 military coup-or-whatever-it-was, there have been reports of greatly stepped-up operations in Sinai. The military characterizes this as a "war on terror," and since the presence of Egyptian troops in Sinai is limited and restricted under the terms of the Egyptian-Israeli peace treaty, one has to presume that there is at least some consultation between the two countries concerning where Egyptian troops may operate. It is also obvious that that is a highly sensitive subject right now. Israel also recently reported a rocket attack aimed at Eilat which was reportedly intercepted by its Iron Dome defense system; Egypt is aware that any attack launched on Israeli territory from Sinai is destabilizing and could provoke an Israeli incursion into Egyptian territory. How much coordination is taking place beyond these considerations is a trickier issue.
The exact scope of the Egyptian Army's operations are also unclear. (And for the purpose of this discussion, the question of whether they are Army, Border Guards, or Interior Ministry troops or even General Intelligence operatives involved is also somewhat beside the point.) Some jihadist claims (which of course should not be assumed to be trustworthy) have suggested that the Army has actually been fairly ruthless in Sinai; it's widely believed that one reason the Army moved was a growing sense that President Morsi was not willing to wage a major campaign in Sinai. But as with so much else, the exact details are unclear.
Major operations by Egyptian forces in Sinai do appear to be under way. Beyond that, expect more sensitivity about any Israeli role beyond that required by the terms of the Peace Treaty, and denials of direct cooperation.