I'm thinking not.
Well it depends...if they are our best pool towels I will wash them because the chlorine staying in them does damage the fabric over time.
The cheaper ones I will just hang out to dry and let the kids use them a few times.
Our pool is very clean and we have a great pool cover which is wound over the pool each night to stop any leaves etc falling in, so I guess that helps.
We had a pool growing up and we just hung towels over the railings, my mom wasn't very 'domestic' so I am sure they didn't get washed frequently.
As an adult, I do not have a pool but the kids go to swimming lessons and we go to a local lake. I don't usually wash the lake water towels every time, we go several times a week in the summer. I think I washed the kids pool towels after 2 or 3 uses.
I wash our pool towels pretty much every time they're used. They're flung on the grounds, dragged on the sidewalk/grass, sometimes dipped in the pool. They're rarely clean/dry enough to be reused. So, I buy a few new ones each year to add to our collection. Even the cheaper Target towels handle multiple washes.
We do reuse bath towels, though.