TL;DR - Not really, and more importantly, they’re not needed.
Tea tree oil is said to have antiseptic and antifungal properties. There’s not really a ton of scientific evidence to support that, but let’s say for the sake of discussion that it’s 100% true. Now here’s something that IS 100% true: using products that kill bacteria on a piercing is never necessary. You have an immune system! As long as you’re a reasonably healthy person, you don’t have to worry that scraping your knee, cutting yourself shaving, or popping a zit is going to kill you. Your body is designed to isolate harmful things and neutralize them. Think about your immune system being the FBI, and your body is America. Your immune system is always on the prowl, evaluating threats, listening to your phone calls, and keeping you safe, without you even knowing. Now, if the FBI was trying to catch a criminal, and knew he was hiding in a hotel, would they call in the Army to blow up the whole thing? Nope! There’d be more harm than good done, right? Well, that’s what it’s like when you use an antiseptic / antimicrobial / antibacterial product on a piercing… Sure, you’re getting rid of the bad stuff, but you’re doing WAY more harm than good. Funnily enough, what we see tea tree oil getting recommended for most often is piercing bumps, which are normally caused by physical irritation! That’s like taking tylenol to stop someone from punching you in the face.
Chamomile makes a delicious tea (I like a little honey in mine) and it’s said to relieve inflammation. Again, there’s not really a lot of science to support that. I’ve seen piercers recommend soaking an irritated piercing in chamomile tea or using a steeped tea bag as a compress. In either of these situations, that tea or tea bag is hot. Guess what heat does? It’s a vasodilator, meaning it expands blood vessels, which actually encourages swelling. Much like with tea tree oil, I normally see chamomile tea being recommended as a treatment for the dreaded piercing bubble. Since those bumps are caused by physical irritation, they need to be treated by removing the source of the irritation, not rubbing something from the health food store on them. Once the cause of the irritation is gone, the bump will be very happy to go away on it’s own.
Sorry for talking your ear off, but I guess people read this stuff enough to make it worthwhile. :)