Native Americans did sometimes use smoke to various extents along with employing various forms of magic and other appeasements to the spirits. Keep in mind that Native Americans were regularly involved with activities the including burning on top of that (cooking, fire for warmth, fire for light, firing of pottery, heat treating wood and stone, etc.). They likely smelled a lot like smoke whether they passed through smoke before hunting or not.
The whole notion of cover scent and scent control success is a really interesting sort of topic with a lot of amazing claims from commerical scent control producers and a lot of anecdotal claims. Aside from your clothing, are you going to smoke your gun and all the other gear you have with you? You can bet that your gun is giving off all sorts of chemical smells not typical to the woods or prairie. Just curious, because you don't want to do an incomplete job, LOL.
People will tell you that X brand scent elimination garment works so well they were able to get close to Y animal. People will tell you an ozone machine works so well that they were able to get close to Y animal. People will tell you Q brand cover scent works so well, they were able to get close to Y animal. You can add Faraday cage suits and certain types of camo to claims as well.
Missing from all this is the animal's perspective. Did the animal smell, see, and sense the human and just not care for some reason? It is really hard to know when something has worked if you don't get the perspective of the animal.
I can tell you that sitting still under a tree next to a trail that I have had deer walk within a few feet of me and not spook. This is without wearing cover scent or using any particular devices, wearing blue jeans and a green shirt.
Let's say you smoke your clothing. Are you going to impregnate them with so much smell as to cover your human scent? Or is it that you will just smell like a smokey human being? Deer have better noses than does and dogs can smell drugs wrapped in plastic bags submerged in the fuel tanks of vehicles. Somehow the strong over scent of diesel or gasoline just wasn't enough.
Play the wind as best as you can. If you can't approach or shoot from down wind, then try to be as elevated as possible that your scent molecules pass above the area where you expect your game to be.