Tracking does interfere with SAR. Or rather, SAR interferes with tracking. Our county has a K9 tracking team that is completely separate from the wilderness SAR team.
SAR is partly tracking, but mostly air scenting. SAR dogs are strongly encouraged to air scent because in real life, people do things like fall off cliffs. I had to set up a ton of problems specific to air scenting for the dogs to follow (such as leaping off a 20' embankment into a big hole full of leaves and then bury myself with wet leaves. It took 8 hours for the dogs to find me.
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That's why the pine mushroom thing is probably incompatible. Mushroom hunting is trained very much like drug detection, where you teach them to find a specific scent and then direct the dog in a search pattern that is likely to result in the desired scent being detected. Mushrooms aren't exactly leaving a track.
On the subject of bitework and SAR, IT'S A TERRIBLE IDEA. I say this after one of the other human bodies on my team went to a conference where a police force had brought their K9 to be "certified" as a SAR dog. She had to set up the problem and hide for it.
It found her all right. And darn near sent her to the hospital. She ended up injured and injured the dog trying not to end up dead. She's a tough gal and has seen a lot of crap, and that's the one time I've ever seen her actually fear for her life. TERRIBLE IDEA.
I'm not sure how far from the handler dogs doing bitework usually are, but in SAR the dog can be as much as half a mile away at times. They work off lead, whereas a tracking dog works in a harness. If your dog is doing bite sports and goes far afield, and you're not around to sort out whether it should bite the person it just found or whether it should just come get you, there are big problems. The K9 handlers who were working the dog that attacked her were nowhere NEAR them and were totally oblivious that their dog was mauling someone that it was supposed to just find. It never went back and got the handler once it found her or anything.