Wow, that's some interesting Trek lore. Too bad Mr. Jeffries isn't around for us to grill him about it anymore. His wiki page says this: "According to Jefferies, the Enterprise was Starfleet's 17th starship design and it was the first in the series, therefore the ship had the number '1701."
It also says his Waco plane is in the Virginia Aviation Museum in Richmond. That's only a couple of hours from me; I'll have to take a look at it one weekend.
Star Trek, was, to a large extent, a Heinleinian space opera, and the technology was at least partially "hard SF", which is why the Enterprise was designed with external engines, etc., although they compromised on so much that we now associate Trek with cheap handwavium: artificial gravity, transporter, dilithium, etc. But as NukeET has pointed out, Spock's death in Wrath of Khan was straight out of Heinlein's short story The Green Hills of Earth, in which a guy exposes himself to a lethal dose of radiation in order to save the ship.