In theory, everything can be grown, but in practice, choices are usually limited by size considerations. The support system for a standard aeroponics system is typically the limiting factor. Foam collars and net cups are usually used to support plants, either by the stem or by the roots, and can only support so much weight.
It may be possible to custom design a setup that uses large net buckets and a reinforced support structure for large, heavy plants, but there is theoretically also a point where the height of a large tree, not to mention the size of its root ball, would become impractical from a cost vs benefit point of view.
