General Relativity says that any "shaking" mass (technically, a quadrupole moment that is changing in time (see [here](https://van.physics.illinois.edu/qa/listing.php?id=204
) for some explanations) will radiate gravitational waves. It doesn't matter what kind of matter you've got, dark or regular, just that it is a "source" for gravity.
That said, the amount of power put out in "normal" systems is ridiculously small, so the timescale for orbital decay is enormous; the earth's orbit decays from gravitational radiation at a rate such that we'll hit the Sun in about 10^13 times the current age of the universe! [Source.](https://en.wikipedia.org/wiki/Gravitational_wave#Binaries
) That's why we've only seen gravitational radiation from extreme sources, like the black hole and neutron star mergers seen by LIGO, or the Hulse-Taylor binary pulsar in which we first indirectly saw that energy loss mechanism.
Dark matter halos around galaxies are pretty symmetric, so I suspect their timescales (for collapse, or orbital decay) are even longer... which is a long time indeed.