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Wrong. You actually have to add enough kinetic energy to make the asteroid's orbit elliptical enough cross the orbit of the earth.
If you did it right, the asteroid will have the right sort of gravitational interaction with the earth to raise the earth into a slightly higher orbit. while itself ending up in somewhat lower orbit, ready to do it again and again. You'd need a super-Newton, or somebody with a lot of computer time to play with, to work out what you actually could do, but they probably they wouldn't start off thinking that they had to get rid of an asteroid's kinetic energy before they started the process
Put enough energy into making lots of asteroids make lots of passes around the earth, and the asteroidal mass could be used as a conveyer belt.
If you routed the asteroid orbits past Jupiter as well , you could presumably end up transferring some of it's orbital momentum to the Earth as well.
Jupiter would end up in a slightly lower orbit, but it wouldn't become a near earth object.