Probably. I doubt the Israelis would be particularly bothered by the distinction - they have shown no signs of recognising such niceties in the past.
There's another possibility that intrigues me. Ever since 1967, if not before, there has been talk of establishing an independent State of Palestine, and most Middle east peace talks have had that in mind as the main objective - for one side at least. What if the Hamas government were simply to declare such a state existed? You have two possibilities.
Firstly, that state could include the territory of Israel. Obvious that would have no basis in political reality, but it would be consistent with Hamas' refusal to recognise that the State of Israel exists. Such a state would not be recognised by anybody except, possibly, Iran.
Second, that state would exclude Israeli territory, and just include the West Bank and Gaza. Now you have a situation that is rather different. Many other countries WOULD recognise the existence of such a state.. and that might just start the ball rolling (terrorist activity would need to cease as well) to the extent that eventually even the US and finally Israel would have to accept it, too. But.. to do that must involve acknowledging the right of the State of Israel to exist. Would that be a step Hamas would be brave enough to take, I wonder? Do they want what would be an honorable peace, or are they only interested in continued violence and the destruction of Israel?