With AMD Crossfire, all outputs will go through the top card. Generally you're limited to 3 monitors, although the recent drivers allows up to 5x1 configuration. You'll have to check the individual card's specs for how many it can do. Adding another card in CFX does not increase the amount of displays.
With Nvidia, you can only run 2 monitors per card so you need SLI for 3 monitors.
As for running a single display, yes of course. You could run 4 cards in CFX or SLI and power just 1 monitor.