It's possible, but I think you are vastly underestimating the logistics involved. You're talking about
1)attacking an (abandoned, admittedly) airport, fighting through zombies in the process. Depends on how many zombies are around.
2) finding a plane they have trained on and know how to fly at the airport - flying a modern plane is hard,and only the most basic principles transfer between models. This is honestly the biggest problem they are going to face, and it really is a doozy.
3) finding sufficient aviation fuel to fill the plane's tanks, and fueling it up. Probably not that hard.
4) Finding a worthwhile target to crash into before the fuel runs out. If you're low enough to visually inspect the ground in a jumbo jet, you are either taking off, landing, or crashing, so you better already have your target in mind.
I suppose they could always just dive-bomb a city, which might meet their qualifications for self-martyrdom, but that is about it, and wouldn't really 'help' the zombies in any way. If their goal is to speed the apocalypse, they'd be far better off with traditional bomb-loaded vans or trucks and attacking barricades or fortified camps.