It seems to me that Hamas will follow the path of Fatah.
They will pretend to moderate just barely enough to get the EU to loosen the purse strings and give themselves legitimacy. They miss the days when they could pretend to have a "political arm" and a "military arm" and the Europeans would happily buy into it. This would in turn pressure the US to moderate its stance towards Hamas, and it would pressure Israel as well.
Like Fatah, they will maintain the terror infrastructure but keep it more clandestine and keep plausible deniability. Islamic Jihad, Hizbollah, Al Aqsa Brigades and probably a Gaza Al-Qaeda will be allowed to operate and be protected by the Palestinian Arab government.
Unlike Fatah, Hamas will try to move the PA towards a more religious direction. It doesn't appear that many Palestinian Arabs will have a problem with that.
There is one other big difference between Hamas and Fatah: Hamas actually cares about the Palestinian Arab people. This of course sounds strange, that an organization that encourages its people to blow themselves up cares about them, but the fact is that Hamas does spend time building hospitals and schools, and the PA ignores anything that could help their people. Admittedly, the schools are meant to be training grounds for the next generation of terrorists, but even so there is a charitable component to Hamas that does not exist in the Fatah leadership.
Although it is a slim hope, this could work to Israel's advantage. After all, Israel has an interest in the welfare of Palestinian Arabs. If they are happy and have jobs and prospects they are far less likely to become terrorists. The only people interested in keeping Palestinian Arab refugees" in camps are the Fatah and other Arab leaders. It is not clear that Hamas would encourage maintaining the refugee camps.
The collapse of the PA is a fait accompli. For Israel to remain intransigent towards a Hamas-led PA will not work to Israel's advantage, and frankly the Fatah-led PA was just as interested in Israel's destruction as Hamas is.
It sounds bizarre, but Israel should take the diplomatic initiative in accepting whoever is leading the PA and make a centerpiece of the policy the destruction of "refugee" camps and building of real towns. The disgrace of the UN-administered and self-perpetuating camps needs to be brought to the forefront; putting not only the UN on the defensive but also the PA, Jordan, Lebanon and Syria for what they have done to the Palestinian Arab people.
A shake-up in the PA can hardly hurt, and it may help. The negotiations with the PA have not helped Israel at all, and Hamas' relative pragmatism may bring an opportunity.