Dart: Does crashing a spacecraft into an asteroid change its course?

The title is "Double Asteroid Redirection Test (DART) Mission".

That question is nowhere on the page, likely because of course crashing a spacecraft into an asteroid changes its course. A flyby of an asteroid also changes it course. (For that matter, a gravity assist by Jupiter also changes Jupiter's course.)

Instead, the stated reason is: "This asteroid system is a perfect testing ground to see if intentionally crashing a spacecraft into an asteroid is an effective way to change its course, should an Earth-threatening asteroid be discovered in the future."

I'm curious to know why they think it wouldn't work.