I am pretty convinced this theory is true. For me, the strongest evidence is in the post-show credits. Both Wilson Cruz (Doctor Culver) and Kenneth Mitchell (Kol) get their own intertitle as full-on guest stars. Culver has a 30-second conversation with Stamets and shakes his head over Landry’s body while Kol is clearly a secondary player to Voq in the Klingon storyline. Meanwhile, "Javid Iqbal" gets this:

He has to share the screen with a bunch of one liners on the bridge crew and the computer of a wrecked ship. Unless Iqbal has the worst agent in the industry, there is no logical reason why the Voq actor would get worse billing in the end credits than actors with much smaller roles. Unless of course he already appears in the main titles
This is what convinced me this week that Shazad Latif is Voq (that theory hadn't even been on my radar until suddenly it was obvious). Here's another bit: working in casting, I have access to various casting databases, between them I can always find a listing for any actor working today. I looked him up in all the usual places, and Javid Iqbal isn't listed on any of them. He also does not seem to be signed by an agent.
I just do not see anyway this unrepresented, off-the-grid actor gets THIS role in THIS project. And if he's as out-of-nowhere as it seems, he would be in the press! Because it would definitely be a great story how he has (essentially) no credits and then booked this part!
If Tyler is a Klingon, the doctor should detect that. Even if the Dr doesn't, Lorca's tribble should.
If that's what the Tribble is there for, that is fucking brilliant.
And the process as I had it described to me doesn't typically allow for that kind of flexibility, although instances of rewrites/additions do clearly happen thanks to that example from
@jamestyler.
It's more the casting process and the timing thereof that I find to be the biggest hurdle to clear in terms of this whole "Voq is Lieutenant Tyler" thing anyway.
I've worked on a lot of shows, and it goes all different ways. Some shows do lock the scripts in advance of shooting and don't change them, not because you can't, but because this is how you will get the best results, if you can pull it off. Obviously the shoot will go better if the crew is given plenty of notice of what they are going to shoot, and have time to adequately prep and plan and come up with the best way to realize the scripts vision. (Some shows now will block-shoot their whole season, so those productions really do have to lock their scripts in advance, because it's going to be shot as one giant piece -- more like a movie than TV. I'm speaking of shows that are shot in the more traditional style of one episode after the other, which I believe is what they're doing on Discovery)
Anyway, I've also worked on shows where the scripts are constantly running late, or being significantly rewritten at the last second, and this is a nightmare. But it happens sometimes, for whatever reason... the writing side is just not going well and the scripts are taking too long to pull together, or maybe the showrunner sucks and is not up to the task of getting this show running smoothly, or the network drags their feet with notes/approvals and throws things into chaos by swinging in at the last possible second with edicts that upend everything (I was once working on a serialized network show with some mystery arcs. THE NIGHT BEFORE we were going to shoot a scene for a mid-season episode, to pay off HALF A SEASON OF METICULOUSLY PLANNED BUILDUP on one leads mysterious backstory, the network exec said they had decided they hated what the reveal was and wanted that character to have a different backstory. This is at the end of the business day, so the writers had to spend that night trying to come up with a completely different idea, that would somehow also fit all the many clues and setup that had already been shot, that could be shot with the cast booked for the next day, in the locations already selected. As you might imagine, they did the best they could, but the resulting new pages were awful. Then these new pages are given to the actors in the morning, and shot immediately. The guest cast was now totally wrong for the way their roles had been reconceived, but it was so last minute, there was nothing to do but have them play these now-severely-miscast parts. And suddenly the series regular is told that the truth of her character is totally different than what she had been playing all year. And she has about an hour to assimilate that before going before cameras and shooting these new big dramatic scenes that she has just been handed. It was bad! But this stuff happens. You would be surprised by how many similar stories I have)
But the most common is something in between: you get a script when it's time to start prep that is pretty close to what you will end up shooting. As prep goes on there will be a handful of significant revisions, but it's good faith -- the writers are legitimately having better ideas as they continue to work on it, and the crew still has enough time to adequately prep for it. Revisions continue all the way through shoot, but getting increasingly minor as it goes along, it's just tiny dialogue tweaks by the end of it.