Of course. But try to find an example where the two organizations have ever cooperated in a conflict with Israel.
Hezbollah is a Lebanese based Shia organization created, largely through Iranian money, out of the chaos of the 1982 Israeli incursion into Lebanon. But the Shia of Lebanon and the broader Levant as a group, have had centuries of conflict with the Sunni of whom the Palestinians are a major regional group. It is worth noting that the civil war taking place in Syria just across the border from both Lebanon and Israel as we discuss this has devolved into essentially a Sunni/Shia conflict for control of the country with a bit of Alawite heresy sprinkled on top . Guess who Iran strongly supports. Iran has even moved a Hezbollah fighting force into Syria.
The Israeli conflict has to be viewed within that larger context.
Again Hezbollah will only act if Iran determines sacrificing it on the alter of the IDF furthers its national interests. I personally think it is far more valuable to Iran as a force in being, but we will know for sure when Israel enters Gaza.
This is a pretty good article. The thrust of it is the need for intervention in Syria (about which I am very suspect), but he also does a good quick outline of the historical loyalties.
From the blog of Elazar Gabay at The Times of Israel
blogs.timesofisrael.com