I think Tyler is Voq, although it's hard to imagine how they could create such perfect human-klingon spy both mentally and physically. He could at least try to bite the neck of Michael or something (since Klingon courting is more "physical"). Tyler:"Sorry, I meant it as romantic gentle bite in the neck. Love you so much, I want to eat you. Humans do that right?" Michael:"Gentle? I need to go to sick bay now....Wait... why do you refer to us as humans? Aren't you..ohhhh, myyy - in Sulu's voice-".
For those wondering why Tyler is too perfect. I have 2 words: "Brain transplant". You first heard it here.
Since Tyler is too perfect as a human, it's still possible he's not Voq. Isn't it possible Voq only died because of casting change? After the pilot the Star Trek production parted way with the actress doing the security chief and choose for this role the guy who was doing the Klingon Voq. Voq is a lot of make up and time and the actor was not available anymore for that role (beside maybe for the final and a few odd episodes). L'Rell took over most of the role Voq would have had.
Another theory. Tyler is Voq but it's also possible Lorca is double crossing him. Maybe he has his doubt about him being a Klingon spy from the beginning or maybe he did a bit further down the road. Armed with this knowledge, he decided to keep the enemy close (name/keep him security officer) and monitor him (maybe sending false info to the Klingon).
A lot of theories and speculation.