Nope. Unlike most events, Burning Man actually makes an effort to lessen the environmental impact. Is it a ton of people living and breathing in one area? Yep, and that is going to be a problem no matter where. Those same people would probably be using more in their daily lives as they tried to be good little consumer cogs. A huge part of Burning Man is the importance of doing without and making do with what you brought with you, and sharing what you have. Sure, there are jerks who go out there in big RVs or people thinking it's just a big party and so not caring about the basis of the event, but the average burner tries to live by the 10 Principles and behave like a decent Black Rock City citizen. Just the peer pressure against trash alone is huge. And culturally there is an emphasis against disposable items, so you won't find piles of Solo cups tossed everywhere like other events.
The biggest impact is, of course, the gas required to get there and get the city's infrastructure in place. When building the city, most of the volunteers actually live out there, so no commuting. And there is a limited number of vehicles allowed inside the event, so most people carpool and share what they bring.
Other than a couple of art pieces such as The Man and The Temple, most art is reused by cities looking for beauty. Other items are recycled. Tents are folded away, and people leave with all they brought with them, then the organization spends months restoring the playa to a condition better than before the event. Much better than recreational campers and off-road enthusiasts who often cause a lot of damage out there.
Is there an environmental impact from Burning Man? Sure. Even going to the gym has an environmental impact, but people still do it. Is the environmental impact as bad as party events like Coachella or NFL games? Nah, because the participants and the organization work hard to be better people that take civic responsibility seriously. Yes, they could do better. We could all do better every day of our lives, but that's where a cultural emphasis on being more environmentally conscious becomes important.
Check out BMO's environmental impact reports if you're like to know more.