What is the possibility of a sprinkler head, which is covered by a tree root and very close to an exterior wall, to cause water to penetrate under siding when irrigation system is turned on over quite some time. Could this result in flooding/damage inside the home/flooring?
Yes that is highly possible. We have dealt with a lot of crawlspace water issues that were caused by sprinklers and not all of them were due to broken sprinklers/piping. Any decent amount of water at the foundation can cause infiltration. A good rain storm can cause this. It’s important to have proper positive drainage away from foundations so water cannot pool.
I don’t quite understand what you mean by a sprinkler under a tree root would cause water to get underneath siding?