Hi Katherine and welcome to the Disney Parks Moms Panel.
My family love to explore different Disney Resort hotels when we visit the Walt Disney World Resort as it helps us to decide where we might like to stay during our next trip.
The Big Blue Pool at
Disney's Art of Animation Resort is gated and requires you to use your MagicBand to verify that you are a Guest at that specific Disney Resort hotel before unlocking the gate and allowing access.
I guess that there is nothing stopping you from asking a lifeguard (if present) if you would be able to enter the pool area to take some photographs although I couldn't guarantee that this would be possible.
I can however tell you that if you do decide to visit this Disney Resort hotel during your visit, you would definitely be able to check out and take photographs in the wondrously detailed courtyards of the Finding Nemo, Cars, The Lion King and The Little Mermaid sections of the Resort. My family has many great photographs which were taken in these areas, particularly the Cars section.
Wishing you a magical trip filled with memories which will last a lifetime!
Emma