Yes drinking pool water can cause vomiting. The electrolytes and other chemicals in the pool water can be caustic and offset the body's electrolyte and acid/base balance. Stop your cat from drinking the pool water. Don't allow him to go outside or get a pool cover to prevent him from drinking this water.
Since this is chronic I would have him examined by a veterinarian to make sure there is not another underlying cause and to determine his acid/base and electrolyte status and to make sure no other damage has been done.
Since this is chronic I would have him examined by a veterinarian to make sure there is not another underlying cause and to determine his acid/base and electrolyte status and to make sure no other damage has been done.