You could argue the Germans did something like the Hansen Plan in the OTL Operation Merkury (invasion of Crete) but here they only dropped one airborne division (7th Flieger) but even this was combined with an amphibious operation.
Unfotuneatly Thegn the Hansen Plan is a non starter for logistical reasons alone. Not to mention the fact that the airborne invasion troops would meet with an early disaster s almost happened in Crete. If the Hansen plan were tried the Germans would have to fly in one division at a time. The initial wave might lland but the follow up waves would be intercepted and decimated as they crossed the Mediteranean and Iraq. Those units that did manage to land would be running out of supplies and taking heavy losses. In days they would be dead or rounded up as POWs.
In short the Hansen Plan has about as much chance as the Unmentionable Sea Mammel
If Germany wants to succesfully intervene in Iraq the only way to do it is to implement Black Gold. The downside is Barbarossa has to be postponed a few more months until early spring 1942 but Germany has much to gain by following this option.