Would the helicopter sacrifice scene from London Has Fallen actually happen?

The simple answer is Yes. The 3 helicopters to which you refer are known as 'Marine One'(the callsign for any USMC aircraft carrying the President of the United States), however unlike in the movie, the three helicopters do not fly in consistent formation, they are constantly shifting positions in an effort to prevent any attacks from the ground (at least any attacks with the intention of capture). Any attack which has the intention to kill the President is also unlikely to succeed, as any potential attackers are unlikely to hit any of the 'Marine One' formation in their first attempt, as the movie would have you believe. If you pay attention you will see the aircraft use flares, and receive warnings for a 'missile lock', which the first downed aircraft obviously did not. In real life an attack on the 'Marine One' formation would be not only risky, but extremely futile as all three aircraft are identical in every way (the only three aircraft to share identical tail numbers). The simple answer is yes, in such a scenario, members of the Presidential protection detail from pilots, to bodyguards are all trained and instructed, to protect the Presidents life at all costs, even if it means giving their own.

TL;DR: Yes, presidential escorts - whether military or Secret Service - are trained to protect the president, even at the expense of their own lives.

Assassination attempts:

Ronald Reagan:

Here's a video of the assassination attempt on Ronald Reagan:

And here is what happened:

First shot fired:

Less than a second later, the Secret Service do what they're trained to do. Agents Jerry Parr and Ray Shaddock grab Reagan from behind and virtually throw him into the limo while shielding him from behind with their own bodies. Meanwhile, agent Tim McCarthy gets between Reagan and the shooter and uses his own body to stop any bullets - note the way he spreads his limbs out to cover as much area as possible:

Tim McCarthy is shot in the chest, but remains standing and between the shooter and the president for as long as possible before he collapses:

Another group of agents, along with Washington DC police officers, swarm the shooter - the cop and military officer are laying on the ground because that's what they have been trained to do (they are not members of the president's protection team); the man laying face down is White House Press Secretary James Brady, who was also shot and left paralyzed from the waist down:

McCarthy survived, and later explained:

If you saw the big picture out there, a lot of people – police officers, military -- were ducking and looking for cover. That's the training that they received. They did exactly what they should have done. In the Secret Service, we're trained to cover and evacuate the president. And to cover the president, you have to get as large as you can, rather than hitting the deck. So I have to say people have asked me, and I said quite frankly, it probably had little to do with bravery and an awful lot to do with the reaction based upon the training. It was a heck of a team effort out there that day. It was people like Ray Shaddock and Jerry Parr, pushing the president into the car, other agents going to John Hinckley and helping subdue him, to help save the life of the president that day.
- CBS News

Gerald Ford:

Manson family member Squeaky Fromme tried to assassinate Ford in California. She raised a handgun and pointed it at the president. She was an incompetent gunman, however, and although her pistol was loaded, there wasn't a round in the chamber, so when she pulled the trigger, nothing happened. Agent Larry Buendorf immediately put himself between Fromme and Ford, rushed towards her, and snatched the gun away. At the same time, the other agents surrounded Ford and ran down the street carrying him until he shouted "Put me down!", at which time they released him and walked quickly to their destination.

John Kennedy:

Unfortunately, this attempt was successful. The event is so well known that we don't need to describe it here, but the relevant point is the famous man who climbed onto the back of the presidential limousine.

The man is a Secret Service agent named Clint Hill. Earlier in the day, he had been riding on the limo's bumper:

But when the convoy moved through Daly Plaza, he was walking along behind the vehicle. When the first shot rang out, he dashed for the limo, then clambered onto the trunk:

Why? Because he intended to use his body to shield the president from the gunman.

Much like Tim McCarthy, his goal was to make himself a large obstacle between the shooter and the president.

Marine One:

The presidential helicopter is known as Marine One, and is operated by the HMX-1 unit of the Marines.

As a security measure, Marine One always flies in a group with identical helicopters, sometimes as many as five. One helicopter carries the President, while the others serve as decoys. Upon take-off these helicopters begin to shift in formation to obscure the location of the President. This has been referred to as a presidential shell game.
- Source

An HMX-1 pilot absolutely would sacrifice himself, his crew, and his craft to save the president. However, my friend - a US Coast Guard officer/helicopter pilot/instructor - says it simply wouldn't be necessary:

The president's helicopter is loaded with so much top secret anti-missile gear that I doubt they would ever need another helicopter to "take a missile" for it.

Yes, but not the way it happened in the film. Using a gunshot as a simile, it would be more like a spontaneous decision made by the Secret Service agent to jump in front of the president and taking the bullet. It wouldn't ever involve someone on the radio saying something like "prepare to sacrifice". Yet another reason this movie sucked.