That is a definite possibility, although I'm not so sure that it was an impact that caused them to separate. I would think an impact would have more scattered the debris.
However, I guess an impact could have at least loosened some material, resulting in the smaller piece slowly separating at some later time, perhaps with gravitational help from the Sun or even other planet that it had possibly passed close to.
When it got closer, in 2001, astronomers realized it wasn’t a single asteroid, but two clusters of rubble orbiting each other.
It’s been classified as a Potentially Hazardous Asteroid, but astronomers have calculated a safe trajectory out for at least 1,000 years.
Since it’s a binary object, astronomers are able to calculate the mass and density of the two asteroids.
New observations from the Arecibo Observatory have mapped the twin objects in tremendous detail.
Researchers using the Arecibo Observatory’s powerful radar have made the most detailed observations ever of a binary near-Earth asteroid (NEA) — two clusters of rubble circling each other — offering new clues about how such systems formed, the properties they share and the dynamics of their motion.
The observations, made by Steve Ostro, senior research scientist at the NASA/Caltech Jet Propulsion Laboratory in Pasadena (who earned his master’s degree in engineering physics at Cornell), Jean-Luc Margot, assistant professor of astronomy at Cornell, and their colleagues, describe asteroid (66391) 1999 KW4 (called KW4). Their report appears in the latest issue (Nov. 24) of the journal Science. The double asteroid also appears on the cover.
KW4, they say, is actually a pair of light, porous clusters of rubble that circle each other as they orbit from a point closer to the sun than Mercury and then outward — occasionally passing very close to Earth along the way.
The bodies were discovered in 1999 but were not known to be binary until they were observed in May 2001, when they came within about 2.98 million miles of Earth — their closest pass until 2036.
The researchers used antennas at Arecibo and NASA’s Goldstone Deep Space Network — the only telescopes with the radar capability for such observations. Arecibo, in Puerto Rico, is managed by the National Astronomy and Ionosphere Center at Cornell for the National Science Foundation.
KW4 is a valuable source of information for planetary scientists studying the formation and evolution of NEAs — as well as for researchers studying how to mitigate the potential threat they pose to Earth. KW4 is classified a Potentially Hazardous Asteroid, but data show that its path will not intersect Earth’s for at least 1,000 years.
Unlike single asteroids, many of whose physical properties are impossible to determine from Earth-based observations, binaries can reveal information about their mass and density by their interaction with each other. The researchers were able to reconstruct the orbit, mass, shape and density of KW4’s two components, Alpha and Beta.
They found an oddly shaped pair of dance partners, with Alpha, by far the larger (1.5 kilometers, or a little less than one mile, in diameter) of the two, spinning as fast as possible without breaking apart, and the smaller and denser Beta wobbling noticeably as it orbits its partner. ...”
https://www.universetoday.com/947/detailed-look-at-twin-asteroid-1999-kw4/