I can imagine that you would be able to collect water at the bottom and manually water the plants from the top.

Then again, not being a closed-loop thing, it would evaporate pretty quickly.
So I dunno. Try it!

If you do it manually your whole day will be consumed with watering schedule. If you use a solar-powered pump, it won’t work at night and cloudy days, unless you invest more in a battery storage unit. So you need a pump with electricity.

Honestly guys, hydroponics is all about constant flow of nutrient rich water. It is different from soil growing where you just soak the soil. The constant flow is what makes the plants grow more effectively. What you can and should do is to put your pump on a timer. You can get cheap timers at a hardware store that will let you turn the pump on for fifteen minutes and off for fifteen minutes. Do this once an hour and most dry-loving plants will be happy. Do it more frequently for wet-loving plants like cilantro or watercress.