Yes, it is correct that clumping can be solely gravitational effect, though so far we have pretty vague idea about the density in those clumps and halos, which are mostly derived from N-body simulation, which are obviously model dependent, e.g. NFW profile [1]. If dark matter interacts with itself one can expect deviations from purely gravitational description due to dark matter analogues of pressure, temperature, viscosity, etc.

[1] https://en.wikipedia.org/wiki/Navarro%E2%80%93Frenk%E2%80%93...