No, you mine from each card independently.
This.
When multiple cards are in your machine they are all recognised (provided the PCI-E Slot they are in can handle them) and the dirver is installed for each of them. Any miner will also recognize all the cards but will use only one for mining. If you want to mine on several cards you have to start the miner once for each card and tell it which card to use.
All that crossfire does is enable the cards to synchronize and split up the rendering of a frame. This is only needed for games, because the snychronization is crucial as the split up work between the cards usually means that card one renders the upper half and card two renders the lower half of a frame. If that renering isn't synched the two halfs do not match which looks stupid.
The result of this is: Depending on availability near you you safe between 6 and 20 bucks in initial costs because you don't need to buy the crossfire bridges when you use the machione in question just for mining and not for gaming.