No, really. This trope is invoked and the tree is actively cultivated by the characters themselves. Summed up nicely by one of the final scenes, where Tylor clumsy tosses a dart behind his back, only to have it hit a dead bullseye.
By the end it seems like it has to be a little bit of both. Even if he were a genius, Tylor stumbles onto situations powered by sheer blind luck while enough hints are dropped that it's hard to buy into him just being a lucky idiot.
The issue with the hints above is not exactly helped by how some actions of Tylor are explicitly strokes of genius (like realizing Harumi is a spyright away), while others are explicitly strokes of dumb luck (like how he survives his execution by firing squad). That means that every hint CAN be taken both ways with canon to back the interpretation up.
There is an old Japanese house-wife tale that idiots never catch colds, and just about any anime sticks with the principle. Tylor once suffered a cold for a whole episode. Breaking tradition, or a hint?
The William Tell Overture plays during the most epic game of chicken ever in episode 23.
Suppe's Charge of the Light Cavalry during Operation: Rescue Yuriko in the final episode.
Badass Decay: Yamamoto. In the second episode he's the leader of the forces assigned to the hostage situation, firmly in control of himself. Things go Tylor's way during the hostage situation, ridiculing him. As such he gets assigned to the Soyokaze and thus becomes rather pathetic in his efforts to control Tylor.
Yet, he also Took a Level in Badass when he took command after Tylor got captured by the Raalgon, deciding to just warp directly in front of the Raalgon flagship and start blasting.
Complete Monster: Prime Minister Naku Ra Wang, the chief advisor for Empress Azalyn, seeks to become emperor of the Raalgon Empire. Using the death of her father, he manipulates Azalyn into declaring the United Planet Space Force as an enemy, resulting in thousands of deaths on both sides. Feeling impatient, Wang tries to assassinate Azalyn by setting off an explosive in her room, which places Tylor into a coma. After Azalyn returns from the Soyokaze, Wang manipulates her and the council into commencing an attack on the UPSF headquarters, planning to win the battle, start a war with the UPSF, and increase his reputation as the war's chief proponent. Six months after his plan fails, Wang tries to start another war with the UPSF by hiring both Raalgon terrorists to cause destruction on Earth, and a mysterious third party to destroy Azalyn's home planet in order to stir up both sides. Once the war starts, Wang launches a coup on the Melva, holding Azalyn captive, seizing the throne, and declaring a full-scale attack on the UPSF Spacefleet.
Crazy Awesome: Tylor is one of the trope's best examples. No one's clear on whether he's a lucky fool masquerading as a genius, a genius using people's opinions of him as a fool to become a chessmaster, A Magnificent Bastard, or a lunatic whose irrational approach manages to somehow always work.
Family-Unfriendly Aesop: Ignore all your responsibilities and do whatever you want all the time and things will turn out for the best. Still, just like Tylor himself, there may be more depth to this philosophy than there initially seems.
Specifically, one interpretation is that Tylor deliberately let them do what they want, get in over their heads, and only be saved by his apparent foolishness by giving a time bomb in a box to the Raalgons they had surrendered to.
It's worth noting that "Do what you want" was the one order the crew wasn't capable of disobeying.
Periphery Demographic: John Ringo apparently loved the series so much as to writenote Together with one Victor Mitchell an even more insane parody of it, a short story "A Ship Named Francis", for the Honor Harrington anthology In the Service of the Sword. On the other hand it was a much crazier and less adjusted ship this time.