He is indeed. And I hope you'll take my word as an okay source until I find links or something for you.
Spenser and I saw him speak at the official Star Trek convention in Las Vegas this past summer, and I know that at least I was amazed with his dedication to the original show. He spoke a lot about his interpretation of Scotty, how it was to be similar and how he wanted it to be different, out of respect for James Doohan. He said something along the lines of not making an exact copy, because then it could be seen as a parody, and he didn't want that to happen. Then he gave talked for awhile about selecting and refining the accent, so it would match everything TOS Scotty's backstory suggested. He also said something about how Scotty does not exist solely for comic relief, and how this is something he hopes to explore in later movies. I know he listed a few favorite episodes and told why, too, but I don't remember which ones D: He is also a fan of Star Trek Continues :)
According to his commentary on the film Paul, which he wrote and acted in, many of the Star Trek references and parallels had to be cut just before post-production, as he had just been cast as Scotty and there was an issue there with publicity. But the movie takes place at a sci-fi convention, then on a road trip. During the commentary, he and the director mention how Borg costumes had to be replaced by orcs, which they were given the rights to, and how they had to limit the amount of times Class M planets, the Prime Directive, and other Trek procedures were used when the characters met an actual alien.
I also feel like in the majority of his interviews, he talks really passionately and knowledgeably about the source material. And you can see Trek things in nearly all of his writing projects, too.
Yeah idk I feel weird like defending a person in this capacity but yeah I think he'd be an excellent choice. If nothing else, I can say confidently that he is more respectful of the source material and the resulting fandom (traditions, inclusion, fan culture, etc.) than any of the reboot's other production staff. Plus he and Edgar Wright have literally perfected the art of character-driven writing. And that's what I want from Star Trek. Not action and explosions; the characters I love.