Most fruit tree are grafted to rootstock. This does not mean that an airlayer will not work. Most plums, apricots, peaches and nectarines are grafted on to a variety of plum.
Depending on the charcteristics of the tree whether it is a dwarf, semi dwarf or a standard tree they usually use different types of plums. I received some native plums from a forum member in Colorado that I will use to graft peaches onto. The native plums have a very hardy root system that will live in many soil types making it a very good choice for rootstock. With that being said, almost all fruit trees can be rooted and live from its own root system. It just may not do as well in your soil as your rootstock. There are several native plums that grow in Texas. You could use the Chickasaw, Munson or the Mexican plum as a rootstock and graft on to them.