Physicist: Just a quick note before answering this; hanging off of power lines holds a special place simultaneously in both in the Very Long List of Stupid Things to Do and the Somewhat Shorter List of Last Things to Ever Do. Hanging off of power lines is a very effective way to get yourself killed a lot.
Assuming the dude in question was in contact with exactly one wire, and absolutely nothing else, and wasn’t even close to touching anything else, and that the wire didn’t snap, then he’d be fine. Getting into that situation and back out again however involves getting electrocuted pretty good. Turns out that the voltage in power lines is high enough that it can jump a fair distance (given the chance).
Electricity is a lot like water, with electrical current being a lot like water current, and voltage being a lot like water pressure. It turns out that for slightly obscure reasons it’s a lot more efficient to transmit electricity using low current and high voltage. So you can think of power lines as being like big pipes that are holding slowly moving water that’s under a lot of pressure, and that are looking for any chance to “spring a leak”.
Being in a high-pressure environment isn’t so bad, but being between high and low pressures is so bad. For example, you can dive to 250 feet (with air tanks and whatnot), and despite being exposed to lots of pressure you don’t get pushed around or hurt. But if you try to hold back the water in a fire hose, which operates at about the same pressure, you’ll get pushed around plenty (also, point of fact, you won’t stop the water at all).
The same sort of thing is true with voltage. If you stand on the ground you’re at the same voltage as everything around you, and there’s no need for electricity to flow through you. And, somewhat surprisingly, if you’re dangling from a power line you’re at the same voltage as the power line and there’s no need for electricity to flow through you. But, if you get close to anything else, the voltage difference may be big enough for the electricity to “make a break for it” and flow through you and out onto whatever you’re near. Same thing would happen if the wire snapped; you’d become part of the wire.
Unlike a lot of the “what if” question we get, this is one that’s been tested very, very extensively, both in terms of safety and danger. If it were dangerous to touch a power line (while not touching anything else), then there wouldn’t be many birds left (or those that were left would wise up real fast).
But since contacting anything else (especially another wire) is dangerous this is a serious issue for birds big enough to bridge the gap between lines. As a result you’ll often find weirdly shaped power poles, or very widely spaced wires in areas with large birds (large flying birds that is).
The people who work with power lines take a lot of precautions. Everything is insulated, so that they don’t ever touch the wires directly, and even if they do, they’re not touching anything else that can conduct. By the way, and I can’t emphasize this enough, as safe and fun as hanging on power lines might seem, it’s both deadly and boring.
The fire hose picture is from here and was taken during a celebration (not a protest or anything). The bird pictures are from here and here.