I know nothing of crayfish, but if he likes to chew on objects and to destroy them, lol, I suppose he'd do the same with live plants?
As for Cichlids in general, it depends on the species. Angelfish and Discus, for example, are Cichlids and they both love planted tanks. Lake MalawI Cichlids, on the other hand, like rocky settings with a lot of stones/cobbles/rocks in their tanks (and I think lots of caves).
The crawfish will destroy live plants just like he does the plastic ones.
Many of your cichlids species will destroy plants also. Like Isabella said, the angels and discus love planted tanks, and the african cichlids prefer rocks. I have a shelldweller tank with lots of live plants in it, and everyone is stumped because these shellies normally bury everything in the tank with sand, but mine aren't the diggers most of them are. Most folks with african cichlids say the fish destroy plants in their tanks, so they don't have them in the tank.
I guess you could keep the plastic plants in (if they can last for a while, that is, lol). And if you don't mind buying new plastic plants every once in a while, why not do that? It'll give some hiding places for your fish, unless you have caves.