It's not totally impossible, but I will have to remove my sidewalk, dig around my gazebo, take out my fence around my garden and dig over five hundred feet to get to where the downward slope of the drain comes out of the ground. If I was just going straight out, level, I could probably cut it down to about 300 hundred feet. My land has a very nice, gradual slope that isn't very steep, but carries water away nicely.
Or... hire a directional borer and have it done in a few hours with very minimal disturbance above ground. But, know idea how much that costs. Probably a lot more than just putting in a sump pump with drain tiles around the footing, with a 1" pipe out of the sump pump to daylight. Perhaps a dry streambed in you landscaping?
The purpose of the drain tiles and sump pit are "in case" ground water shows up. Or, "in case" your basement would ever flood (broken water pipe, washing machine overflow, freezer defrosts, etc...). Its and insurance policy. They are required here, but most remain dry for their entire life. My in-laws' have their washing machine drain into one, and that pumps up and into their septic system. The other one is for the drain tiles and has never ever been used except for the condensate drain on their ed-humidifier in summer. In winter, they'll dump a bucket or two of water in it just to make sure it works.
What you're planning is kind of an experiment. I lived in and experimental house for 24 years (my father's on-going architecture experiment). We had all kinds of un-tried things/systems/materials and he changed them often. It was constant work. He did that purposely to learn, but a few unintended consequences made for a few unpleasant experiences.
You know 100% that a traditional footing, poured walls, drain tiles, waterproofing, etc... are tried and true. You're pretty sure what you want to do will also work. But do you want to find out with concrete? Its pretty much permanent.
Good luck, though. I've seen your work. If anyone can make it work and look good, too, its you! :thumbsup: