Air layering is used when the stem cannot be easily bent down to the ground for ordinary layering. Both types of layering recognize that some plants are hard to root and will root more easily if instead of cutting from the plant and taking the risk that the cutting will not produce roots we leave it attached to continue growing. The host plant then performs a "nursing" function, keeping the layer alive while it simultaneously strikes roots.
The casing is not attached like a tourniquet that cuts off flow of nutrients, just sufficiently tightly to stop the rooting material from drying out. So yes, there is still transport of nutrients happening under the casing. Sometimes it is necessary to "damage" the tissues under the cased area, but only enough to expose some cambium, leaving the majority intact to support the shoot.