Yes. It is in fact already escaped from the earth and is influenced more strongly by the sun's gravity than earth's gravity. Eventually it will cease even the appearance of circling earth and will assume a position in earth's solar orbit either 60 degrees lagging or 60 degrees ahead, but there will be an intermediate orbit that carries it far away and brings it back in a horseshoe shaped orbit until that happens.
More Moons Around Earth? It’s Not So LoonyOctober 29 1999 -- Earth has a second moon, of sorts, and could have many others. Cruithne, the 3-mile-wide (5-km) satellite, takes 770 years to complete a horseshoe-shaped orbit around Earth, and will remain in a suspended state around Earth for at least 5,000 years. Every 385 years, it comes to its closest point to Earth, some 9.3 million miles (15 million kilometers) away. Its next close approach to Earth comes in 2285. "We found new dynamical channels through which free asteroids become temporarily moons of Earth and stay there from a few thousand years to several tens of thousands of years," said Fathi Namouni, one of the researchers, now at Princeton University. Namouni’s colleague Apostolos Christou said, "At specific points in its orbit, it reverses its rate of motion with respect to Earth so it will appear to go back and forth." In his view, there are three classes of moons – large moons in near-circular orbits around a planet, having formed soon after the planet; smaller fragments that are the products of collisions; and outer, irregular moons in odd orbits, or captured asteroids like Cruithne. In the past year, astronomers have reported finding such objects around Uranus.
by Robin Lloyd