I've never done what you plan to do, but I have used large fabric pots for tomatoes and peppers for five or six years. I think the greatest advantages from using them come when you place them directly on the ground. That way they act like mini-raised beds, with the earth acting like a giant wick. They never have a perched water table, and you can use a heavier potting mix that doesn't require as frequent watering as the faster draining mix you need to use in a more conventional container. When you place them on a solid surface and wrap them in a different material, they become more like a conventional solid container.

When I water them, the sides of the container weep water. That's how I know I have thoroughly saturated the soil. I use 5-1-1 mix, which is mostly pine bark fines, so the runoff probably isn't as brown as something like MiracleGro potting mix or mixes with compost or manure might produce. But, I expect there would be some straining on your deck. Also, my fabric containers are not what I would consider very attractive. The top few inches fold in and they appear a little lopsided. I love them, but I wouldn't recommend them to someone who cares a lot about the aesthetics of their deck.

I grow dozens of fruits and veggies in fabric bags, from 1 to 60 gallon Root Pouches. I love them and think they're pretty good looking when they're filled up completely with soil. If you don't fill them up, they look a little floppy.

I also put some of my fabric pouches in square planters. That way they get their roots pruned, but it looks a little better. Here's a pick of a dragon fruit in a 15 gallon pouch inside wood planter with trellis (banana in a 60 gallon root pouch behind it):

If you use "Soil Less" potting mix (recommended), There won't be any MUD coming out. Mud can come IFF you use garden soil and/or compost.
But , then again, for container growing soil less medium is the norm.

Actually, to think about it, less solids should come out of fabric bags than conventional pots with drain holes.

Seysonn