I'm not sure if K9s were brought in IMMEDIATELY but there was at least one (
TMZ - Border Patrol K9) brought in by border patrol after ransom note #1 was received. Their dogs are often cross trained in multiple different "fields" of scent detection.
My girl specifically is trained for live tracking, so the sooner she can get on a scent the better. K9s trained for search and rescue not only work on the trail, they also can find objects with the scent on it which often helps confirm you are getting somewhere. My girl doesn't focus heavily/too long on "dropped" items so you've got a real quick window with her to note it and flag someone to get to it. The science of scent is incredibly fascinating (to me at least) but based on wind patterns and where a scent can "pool" (settling into crevices/dips/brushy areas/etc) you can get an idea of the direction often. If the wind is insane it complicates things. Other weather can enhance/lessen the scent. Thanks to where we live, my girl has trained in crawfish ponds and a foot or two of water, so it can really depend on the surfaces the dog has trained on, as well as the age of the track. Sooner a dog hits the ground running, the better obviously.
My 2nd K9 is training for HRD (Human Remains Detection). He's an idiot mutt and is insanely high energy which is what you want in a dog to cut loose to make a body recovery. These dogs often work a specifically outlined area and they usually run the perimeter and slowly circle in to "clear" an area. These k9s aren't looking for anything but the scent of
HUMAN decomposition. Not dead animals, not rotting food, human decomposition only. I have seen dogs in boats locate bodies under water from the gases that come up out of the water, I've watched a Malinois damn near climb a tree to get to training remains located 12-15 feet up off the ground in the tree branches.
Like I mentioned above, before I started rambling about k9s (SORRRRRYYYY Y'ALL) a lot of military and LE handled dogs are cross trained. Our organization chooses not to cross train because we've found that our bloodhounds actually get pretty depressed for several days after making a body recovery. German shepherds, Malinois, Dutch Shepards don't get bothered as much because they are motivated by a different reward, which is why you see more of these dogs in military & LE. Less dogs to house/feed/train. But a bloodhound will always be the superior tracker
To go back to the point of NG's case, not only could/would tracking dogs have tracked for NG, they also could pick up a scent off anything a perp dropped/touched/walked through. As long as they've got a starting scent, dogs will go. It's on the handler to decipher their signals. My girl gets really upset when she loses the scent (ex: scent took off in a car) and it's obvious she's lost it. She also does a "proximity alert" when she is right on top of an abundance of scent and she can't quite pinpoint where she wants to go because the scent is so strong and overwhelming. I've watched her look at her "find" straight on but she waits on her nose to confirm the person she is staring at is the one she's looking for. Just because my k9 isn't trained for HRD doesn't mean she doesn't sometimes make a recovery and not a "rescue". You just never know.
At this point with NG if we see dogs again I would expect to see them in a very specific location that is NOT NGs home. Whether they would be looking for suspects, a body (eek), or evidence, at this point they wouldn't be combing through anywhere other than a place they had good reason to believe one of those things would be & it would look pretty different than what an initial k9 search/track would look like.