Yes they can smell your trail, and, they can smell where you handled the caller and set it up. I've seen it, been burned by it, and now will ALWAYS try to shoot the coyote BEFORE he gets to the caller. Several times before I figured this out I had coyotes run to the caller and decoy with mouths ready to chomp down on my deke when they acted as if they had run into an invisible wall when they got a whiff of my scent. Their reaction was as if someone had swatted them in the face with a tennis racket when they smelled the human odor on the equipment. I used to spritz some coon or fox cover scent around the set and on my back trail. Didn’t seem to matter one bit, the coyotes still made me in about a half second when they got close to the gear. I've watched coyotes from a treestand while bow hunting deer cross my backtrack; there is no mistaking when they hit your scent trail. Some of those coyotes have turned and trotted off looking around wildly as they go, others get sneaky and slink away through the brush like a ghost.
Years back while deer hunting during the firearms season I was sitting out on a point that watched a big flat white oak bottom with a creek that ran down the middle of it. The wind had shifted and was blowing at my back now instead of my face. However, I was real certain any critter would have to get out in the middle of the oak flat before it could catch the scent cone and by the time it did I could have a decent shot. I caught movement coming from my left down the holler. It was a coyote following the creek bank. I watched it with interest to see where it would smell me. Just as I thought the coyote got darn near straight in front of me before it caught my scent. The reaction wasn’t something I expected though… That coyote was just ambling along, nosing around, when suddenly it threw its nose up and for about a second stopped still. Then it jumped behind a large log that was lying along the creek bank and lay flat. From my elevated position I could still see it lying tight behind the log. That old coyote eased its eyes just over the log and looked right at me. It was still as a stone for about thirty seconds, then it turned around very carefully and using the log as cover slipped down into the creek bank and reversed itself traveling back the way it came from under the overhanging bank of the creek. That was a sly coyote for sure and a great example of how crafty they can be. A doe came by later and when she hit my scent she flagged and loped on in the direction she was headed, crossing the scent trail. A small buck came by about five minutes later and showed no visible reaction to my scent as he trailed the doe. An old woods wise whitetail doe is pretty slick too. Bucks in the rut much less so… which is off topic, sorry for the ramble.