The answer is yes. But not for everyone.
The first two people on record to die on Everest were George Mallory and Andrew Irvine. There's speculation that they may have even summited the Mountain, making them the first team ever to conquer the tallest mountain in the world, and almost 30 years before Sir Edmund Hillary and Tensing Norgay made their successful summit.
They were last seen only a couple hundred metres form the summit, but never made it back down to the bottom. For decades people wondered if they may have made it to the top, but the only way to confirm that would be to find the camera they took up the mountain with them, and develop the film to see if they had taken a summit picture.
In 1999 an expedition was led to search for their bodies, and against all odds, they were able to find, and positively identify the body of George Mallory, who appeared to have suffered a fall and broken his leg. His body was found almost perfectly preserved (aside from being bleached white by the sun).
Andrew Irvine's body was not found unfortunately, and he was the one who was carrying the camera.
There have been other expeditions to retrieve bodies off of the mountain, there is a foundation in Nepal dedicated to cleaning up Mt. Everest, and to date have retrieved tonnes of garbage off of the mountain, and they collect some bodies as well, but most people request that the bodies of their fallen loved ones be left on the mountain.
For the Most part, extractions are impossible due to the extremes of being at such high elevation, and bodies are left exactly where they fell if they died in the death zone, except for bodies which lay right on the trail, those ones tend to get pushed over the side of the mountain, or they're left on the side of the trail and the 200km/h winter winds will blow them off the edge in the off season, the rest just stay where they are, and will likely remain there, preserved for years to come (just like George). There are over 200 bodies on everest, and that number keeps climbing every year as people line up to go die on the highest summit on Earth.