Imagine someone who could do everything Lars Andersen can, but with even more accuracy and power, in addition to being very strong and athletic and being able to do it with a heavier bow and faster arrows.

Is it plausible that in the modern world, this person could, or rather would be utilized in military conflicts? This question - How to explain the use of high-tech bows instead of guns - is similar, but asks how to modify the world to suit the premise.

In this question, I'm not looking to "explain" it by changing the world, but rather asking a - more or less - yes or no question. There are no archers on the battlefield today (as far as I know), but if there was someone so skillful at archery, could he be of use in a modern military scenario?

Current archers in Modern Military

China

Believe it or not there is still one archery unit in a modern military: The Republic of China's Mountain Company. This unit uses bows in dense forest, heavy underbrush, mountainous terrain for its stealth (usually with ambush or hit & run tactics). I don't know of any other unit which just uses a bow but China does use crossbows for a number of operations (usually border & civilian suppression) as in:

For instance, below is a Chinese Special Forces unit displaying a crossbow used for suppression:

^{Crossbow for suppression}

^{Border Patrol training with crossbows (bolts are less likely to set of explosives when you hit someone)}

Vietnam

Also, certainly within the modern time frame, the Vietnam war saw the Montagnards (native group) working with the US military used crossbows against the Viet Cong. The Green Berets were rumor to have also found these effective for ambush and hit & runs and used them when working with this group but I never found someone who collaborated this (they were given as gift but GB said he never used it) but have heard numerous stories of Montagnard usage.

World War II

Now WWII might or might not be modern, and this might not count but have to include it. There was this crazy guy named Jack Churchill who actually fought with a longbow (& broadsword while playing bagpipes). This was not due to any tactical advantage but was a moral booster.

Other modern usage

Military groups have really removed the crossbow & bow as assassination weapons (rifles are just better due to range) but they are still used in jungle combat, with special forces, and as riot equipment.

^{Peruvian unit (note jungles behind them) in formation with crossbows}

TLDR;
Any heavy camo area (jungle, forest, etc) where the silent aspect of the bow/crossbow is vital to the tactics small units use is the current usage in the military.

Yes

Modern warfare is characterized by asymmetrical warfare, not so much by technology. Combatants in the middle east with little to no technology can evade America's drones, cameras, satellites, bombs, etc, by constructing and using caves and underground tunnels. One of the biggest challenges America faced in their war with Vietnam was not their technological or militaristic strength; it was the Vietnamese terrain, the local's knowledge of the area, and politics (the US could not bomb outside Vietnam, so the Viet Cong used the Ho Chi Minh trail which ran through Laos and Cambodia).

The point is not whether or not he could be of use, but in what situations would he be of use?

Black Ops and Assassinations

Guns are loud. REALLY loud. Silencers don't do what Hollywood makes you think they do. There are small guns (sub-22 calibre) that can be made to be "silent", but they aren't lethal. This makes them rather impractical, because you (a) have to be close to the target and (b) would probably be better using a knife at that point so the target doesn't scream. If assassinating a high-profile enemy target, a really good archer could get "close enough" - being upwards of 50 or 100 yards away - and make a lethal shot with a silent arrow.

Furthermore, because arrows don't rely on explosives, they'd be easier to deconstruct and take through airports, across countries, hide in cars, evade detection by police dogs (who are trained to sniff-out explosives).

Any type of assassination or black-ops situation could make use of such a skilled archer for the simple advantage of sound - he can move quickly, strike targets, and not reveal his location. Even simple issues like navigating through a forest would allow him to kill and eat his own food without risking the gunshot being heard miles away. This makes him a silent predator that can quickly enter (and leave) difficult terrain silently. Or, rather, he can camp out in difficult terrain silently.

Civil Unrest

Suburban warfare is hell for everyone - if a governing party doesn't (or can't) blow up a city, and that city is extremely hostile, every single building because a potential hiding spot, explosive, etc.

Without the "boom" of guns, an archer on a rooftop can hit a target without making it obvious which building he is on. He can even release the arrow and run away before the arrow makes the impact. Not relying on gunpowder makes him especially dangerous, as he can either recover or manufacture his own arrows with relative ease.

As far as I know, what Lars Andersen does, has more in common with stage performance then with bow shooting. In order to achieve such speeds, his bow has extremely low draw weight. I can't bring any scientific proof, but I think it's biomechanically impossible even for a fit human to achieve speed, accuracy and projectile velocity with a bow to be on par with contemporary firearms.

There are additional problems with bow and arrow as compared to firearms in the modern battlefield conditions. The whole configuration itself is quite bulky - bows are pretty long (even the short ones), arrows are long too. It's much harder to shoot a bow from cover - you need to take a specific, comparatively exposed position and need space to spread your arms.

Additionally, if we are speaking about battlefield usage, although arrows may have a chance against soft armor, they pose very little threat to trauma plates.

So, the only scenario where bow and arrows can be useful is ambush (or assasination, as AlexP says), where your target isn't armored, doesn't expect an attack and you have at least one chance to loose a heavy broadhead arrow to disable him quickly. If your targed is armed or has bodyguards, the chance of follow-up shots are very low. If you have multiple opponents, you're better to have numerical advantage.