Hi there anonymous,
Going to Burning Man to meet business contacts is a terrible idea.
Going as part of a camp arranged in advance and putting sweat equity into that camp with the 'right people' to become better friends with business contacts you already know is maybe a better idea, still seems kinda fake. However, if you don't already know VC and tech exec people...you're not going to meet them at burning man (more below). You'll also be pretty exposed and come off as fake due to burning man's culture. It'll be a waste of money you could have spent on your startup or attending an event designed for networking like Tech Crunch or NewCo festival. Note that budget to attend is between 1500-3k for ticket, supplies, transport, etc.
Qualifications for my answer: I'm a long time 'burner' and attended in '04, '05, '06, and '13. I wrote my undergraduate sociology thesis on Burning Man in '04 as an outsider to the community. I got a masters in Engineering after.
Why would going to Burning Man to meet business contacts be a bad idea?
It is frowned on to talk business or any commercial interest at Burning Man. That's likely why many tech execs have been drawn to it, the disconnection from 'reality' where everyone wants something. Being that guy who wants a business card, or to be your friend after working real hard to learn you work at a VC, or an email, or to meet after the burn, or whatever is totally not cool.
How does the disconnect work:
Social Status changes. In the 'real world' people ask what you do, how long you've lived somewhere. Professions and communities give status. At burning man, asking what someone does for a living is largely frowned on. No one wants to talk about it. This just leads to conversations that are routine and boring and you've had in a taxi or networking event ten million times already. Instead, usually what is asked is what camp you're from and what your camps contribution is (giant art sculpture, dance club, social venue), how many burns you've been to, and what of all the amazing art eye candy you've enjoyed the most and recommend others check out. Whichever camp has the coolest contributions to the playa is how status is derived. This is similar to the native american concept of a pot-lach (now called potluck in americana) where whomever donated the most food or horses to the event got the most social status at the event. Example: in 2004 one camp from belgium built an amazing 4 story dance venue without right angles the entire week. Everyone called it the belgian waffle. Anywhere they went during the week, if they said they worked on the belgian waffle everyone gave them accolades, a big hug, shots, food, whatever.
Money goes away. Nothing is sold at Burning Man. Selling stuff gets you kicked out. 99% of transactions are gifted (think sandy warm drinks at bars, food, etc). The barter economy in my experience is only for some very rare things (trading a handle of booze for a fight in the thunderdome or a ride on a roller coaster).
Names go away. Because of the above two things and the desire for disconnect, many people create playa names and alter egos. While this has gone down in popularity just because of the number of noobs who don't know or are less invested in the event, I would imagine its popular among business contacts you'd target. Imagine if you have a net worth of over 10M and are doing Ecstasy on the playa, you won't give your real name and will create an alter ego. Good luck finding "dusty unicorn" (#gristtrollsburningman) on LinkedIn.
You can definitely try and go to the event to 'befriend' the right business people. This is a tactic that will likely be spotted. I'll conclude with my interpretation of Dale Carnegie here: by attending with a real approach to having a great time, appreciating great art, and making friendships due to connections with people regardless of their status in the real world, you'll be a human people actually want to connect with and that will get you the intros you will need to grow your startup or network.