I've never had this issue, as far as I know none of my animals try, and I don't use any real branches aside from manzanita and the jungle vines. Basically what I'm saying is I have no personal experience with bark chewing. I can't see the vines being a problem; even if the coating isn't a degradable product it's still small enough to pass (not that it's great or anything, but it should pass through). As far as bark and vines go, I'd still keep an eye on it. I'm pretty laid back too as far as over-analyzing every little thing with these animals, in fact too much of it and I'd imagine much frustration and anxiety which isn't what keeping chameleons is about! However, we must still remember that what works in the wild doesn't always compare to life in captivity. A chameleon in the wild can chew on as much bark as it wants, but that doesn't mean it's 100% going to live through the process. Sure it'll probably be fine, but there is always that slim chance something goes wrong-such is the way of life.
This very incident happened not too long ago (I want to say 1-2 years).....a post came up on the forum that the OP's panther cham was salivating profusely, then passed away that day or the next. The culprit ended up being a good chunk of bark that got caught in it's throat and choked him. If someone can find the thread (I can't haha), that would be totally appreciated and IMO very appropriate for this subject.
Again, I'm NOT trying to scare you, as again, that's not what keeping ANY animal is about. Just keep these things in mind, and make your own judgement based on what you know. If it happens once in a while, it's probably nothing. If it happens all the time, it's worth paying close attention. In either scenario I would keep an eye on it, and if it becomes a real problem you can always try different wood or branches made of different material.