Israel has a top 10 army in the world, likely the best army in the Middle East (or at least the second best after Turkey) and by far the best Air Force in the Middle East (and maybe the second best overall after the US). They should be able to invade Gaza while fighting Hezbollah.
Just that it might be bloody for them considering that Gaza means urban warfare, while Hezbollah would fight a guerirà war. Both give significant advantage to the defenders.
Still, I think that if Hezbollah attacks in mass, Israel will occupy Southern Lebanon. Throw Syria in the combination, and Israel still wins. Of course, the more actors, the more damage to Israel, and consequently, the higher chance the US gets involved. And the more state getting involved means it becomes more unpredictable.