Aeration mixes air into water. Aerators also use air to move water vertically, creating currents, allowing mixing of bottom water with top water. Often, this action also generates movement and mixing of nutrients into the water column.
All that to say this...rooted aquatic plants aren't likely to be controlled using aeration alone. But, once plants are gone, consistent aeration can keep water moving, suspending nutrients into the water column, rather than letting all that plant food sink to pond bottom mud, feeding rooted plants.
Plants tend to go away in winter. If they don't prepare to rid the pond of them, and use your aeration system to maintain consistent water quality, with nutrients tied into plankton, rather than macrophytes.


Teach a man to grow fish...
He can teach to catch fish...