you can feed them the flesh but probably not the seeds. Watermelon has very little nutritional value though so think of it as a treat. Here's a great food to feed your galah
Also don't over feed watermelon because it's mostly water. You don't want watery dropping. I only give Ozzie (my alexandrine) watermelon during the hotter days. Most of the time I freeze watermelon in the freezer, and give it as a frozen treat on hot days. Because if I give Ozzie a piece of fresh watermelon, he waste like 95% of it, he only drink the juice.