YES you can take a helicopter to the Mt. Everest summit.
But it has some limitations. Most helicopters are designed to operate at around 10,000 feet.
Helicopters depend on its rotors to generate enough lift to support its weight. At higher altitudes, the air become thinner and its hard to get enough lift.
As Mt. Everest summit is at 29,000 feet above sea level. The air pressure is about 1/3 rd there in comparison to that of at sea level. But we need same lift as needed at normal level to safely operate the helicopter. For this the rotors need to be larger and engine stronger with overall weight as small as possible.
Highest Helicopter Flight Altitude
On June 21, 1972 Jean Boulet of France piloted an Aerospatiale Lama Helicopter to a record altitude of 40,000 feet. He removed all the unnecessary equipments and he was breathing supplimental oxygen.
At that altitude the engines broke and the helo has to be brought down with autorotation.
Helicopter On Everest
Pilot Didier Delsalle succesfully landed an Eurocopter AS350 B3 helicopter on Mt. Everest in May 2005.
So in short you can take a helicopter to Mt. Everest, but its not very common.