If, as is theorised, dark matter interacts by gravity, then there is certainly no reason why that shouldn't be the case. As to whether dark matter inside a BH would cause any different effects from ordinary matter, I don't see that it would. Dark matter does not interact with ordinary matter apart from through gravity. As gravity is the dominant force inside a BH then dark matter would be treated the same as anything else.
Bear in mind, though, that we don't know what goes on inside a BH and we don't know a lot about dark matter (we don't even know for certain that it exists) so any speculation is purely that - speculation.
What are your views on this?