Hello! Pampas will indeed give you privacy (when in full bloom) but be aware that it does get quite wide (3-4'). Since you cut it down to about 18"-24" in the spring, you lose the covering for a bit, but I doubt you'll be using the pool during that time, anyway.
As for the reed shoots, I'd leave the grass up. It's absolutely beautiful in the winter time. Hardy Pampas does better if you cut down in the spring (like most ornamental grasses).

We may be running into some confusion with common names. Pampas grass, Cortaderia selloana, is not considered reliably hardy below zone 7. Some have grown it successfully in colder zones but it requires significant winter protection and will not achieve the height it does in better suited climates where it is not cut back to the ground each season. It also has extremely sharp blades that can cut like a knife, so perhaps not the best choice adjacent to a pool where kids may be running around with a lot of bare skin :-) Also a bear to deal with when you need to groom or cut back. And except for the flower stalks (which may or may not be present in colder climates and with routine cutting) it doesn't produce any reedy stems.

Hardy 'pampas grass', aka Ravenna grass, Erianthus ravennae, would be a friendlier, more climate appropriate choice but there are other tall and fast growing grasses that would make a good screen as well. Miscanthus sinensis var. condensatus 'Cosmopolitan' or 'Cabaret' are stunning variegated forms that reach impressive sizes (to 10') easily in the growing season. Arundo donax or giant reed would also fill the bill and it will provide the reedy stems you desire also. And all have a much softer, kid-friendly texture.

I agree with gardengal48.

Erianthus has extremely tall flowers but the foliage isn't tall enough to form a great screen. I'd second the recommendation for Miscanthus. Personally, I'm partial to 'Morning Light', which is stunning when backlit, and unlike 'Cosmopolitan' and 'Cabaret' has narrow leaf blades that shed snow and ice well, if you care about winter appearance. The flowers are stunning, too.

Don