Yes, a similar mission in the Middle East would help alleviate terror attacks. If every Christmas since 1952, the U.S. Air Force has airdropped gifts over the islands of Micronesia, making it the oldest ongoing Department of Defense mission, then the islands of Micronesia are undoubtedly more positively inclined towards the United States. A similar mission would help with the Middle East situation.
The people of the Middle East are already terrified of American planes and drones because we're killing people every day over there. Dropping presents instead of bombs and missiles for one day isn't going to help ease the tension from the other 364 days. This sounds like an idea that sounds good in the office of some senator but would flop in the real world.
First, I don't think a fw presents will much of anything to alleviate terrorist attacks. The problem is the ideology. Through a certain group's interpretation of Islam, it is okay to kill people through terrorist attacks. While airdropping gifts is a nice sentiment it only puts a band-aide over the deep complex issues that are eing dealt with in the Middle East at this time.
One of the things that people in the Middle East claim about the United States is that we are a rich country trying to control people. While people on the ground might appreciate gifts from the United States, it will do nothing to alleviate terrorists attacks as it will be another sign we think we are better.