I'm afraid that normal rain would turn your planting pots into soupy mud baths, that is if they were normal pots. Your system
could work if the pots were tall enough that the water could drain down to the 1" level and the roots would stay well enough away, but then you have containers that could tip over in the wind. Also, there would be a lot of soil and that means heavy planters. Dirt is heavy. Wet dirt is really heavy.
One advantage I see to growing containerized plants on floating docks is that you have no shade. Clear, unobstructed sun when the sun is out. But, at the same time you probably have a clear area on land that could provide the same.
What you're trying to achieve really sounds like a greenhouse sort of thing, but I'm certain you already know that. Your question is part of your exploration into how you can make productive use of these otherwise unused floating docks. Have you explored aquaculture? Tilapia? Freshwater shrimp? Catfish? The docks would become feeding platforms, OK, that's off-topic.
Hey, here's a couple ideas that WILL work that are related to your original question of not allowing the drought-sensitive trees to dry out. Now, these are not original ideas in any way. Watering systems for plants have been around since the beginning of time. You're exploring systems that will work out on the floating docks. We can assume no electricity, or you would just install a pump and tubing, conventional. We can also assume you would like this to be a 'no babysit' system (self-watering).
Hydration crystals would be one option, synthetic chunks of an inert substance, mixed with the soil and when watered, they swell with water, hold the water and then release the moisture into the soil at a rate similar to the rate at which water is being removed from the soil (evaporation or transpirational uptake by the trees). They're termed crystals, but they're not really crystals, they just sort of have that appearance in their dry state. Once fully hydrated they look more like chunks of clear jello. The wetted crystals keep the soil in a sort of equilibrium, where the moisture content of the crystals and the surrounding soil remain more or less the same. As the soil dries, the crystals release water to bring the moisture of the soil back up. If both the crystals and the soil eventually dry out, your roots can dehydrate and the trees die. If it rains, or you water the soil, the crystals pull water from the saturated soil and re-swell. This system requires some babysitting, but a lot less than soil alone.
Another viable floating dock system, similar in concept to your cappillary action idea is 'wicking'. To fully get this concept, take a strip of paper towel. Hang it so only the very bottom is submerged in water. watch what happens, the water spontaneously works it's way up the strip, against the force of gravity, until it reaches the top. The strip will maintain more or less the same level of moisture, as long as there is part of the strip in contact with water. Cotton works well, you can tear up strips of old cotton bedsheets, much more durable than paper towelling. You could even use strips of old bath towels. If the soil surrounding the moist strip is dryer than the strip, moisture will move spontaneously into the drier zone and more moisture will be drawn up the strip. If it rains and the soil saturates, wicking action stops.
When it comes time to permanently move the pots, or transplant, just cut off the strip at the bottom level of the container. The tree will do OK with the strip remnant in there and it will eventually decompose. Your 200 trees could each have their own wick strip, but it doesn't take a pond to set up a system like this.
Possibly hybridize the sytems. Wicks and hydration crystals. Overkill, for sure, but the moisture will be constant and consistent.
Will this work? Evolution says soak, drain, certain degree of moisture diminishing until the next soak. A perpetual moisture system should be the same, except for the soak end and the drought end.
My suggestion is consult someone who has actually done your projected system with your particular specie, otherwise you're customizing a particular system and seeing how it will work, learning based on direct experience.
Here's a link to those crystals. This companies call them
Garden Gel and they talk a bit about their use in trees.