Depending on the crayfish, this may or may not be any issue. Some large "yabbies" (which actually encompass a large number of Aussie crayfish that can display blue coloring, either recessively or dominantly) and cichlids/catfish/etc are easily kept together without much issue. Some are not, however. And NA blue crayfish, like the commonly sold P. alleni, will easily and happily take down small cichlids, bottom dwellers and anything slow. However, they don't reach the size that many Aussie species do, so eventually they're likely to become food to your cichlids.
It's your choice to spend the money or not, but ID the species first, because that'll save you some $ and effort from the get-go. (What size tank do you have, too, you may not have a large enough tank for some of the Aussie species, which would also be another issue to consider)