I would think the screen would be a permanent barrier. We are know required to supply, at back of house, a receptacle inside and outside of cage. AHJ says the required back outlet inside of screen is not accessable to the rest of outside. If they require an outlet inside and outside of screen enclosure because of accessability, then the screen would be considered a barrier. Plus it's not considered the required within 20 foot rule if outside the screen enclosure.
I laugh at the requirement of a receptacle within 20 foot of pool, but greater than 10 foot, unless physically impossible to keep 10 foot (680.22 A.4)than 5 foot or greater is OK. Why require an outlet and potential hazard with (680.22 A.3). Swim at your own risk!