Nope. The standard model says nothing definite about the nature of dark matter nor does it predict its existence. Dark matter might be composed of axions; then again it might not. We just don't know.
Comparing gravitational radiation with EM radiation is not terrifically useful - it's unlikely we'll ever be able to throw enough mass around to generate detectable gravitational waves.
Dark matter must exhibit gravity, even if it is non baryonic because it has mass and interacts with the universe. The whole reason for it's theoretical existence is due to the missing mass that must explain velocities that otherwise would not make sense.
If it exists, of course.