Don't plant near the edge of the pool and use mulch in winter.

Strawberries should always have mulch. It keeps the berries clean..... besides all the other obvious benefits. Straw was used before we had woodchips and ground bark.

I'd be wondering about drainage and aeration.

Good point. The container gardening speaker said putting holes in the pool was a must. I was hoping to score a leaky one when I posted a request on Freecycle.