Nope. A half-press of the shutter results in a lock, so you can recompose. Pressing the rest of the way nails the moment without lag. Just a matter of good autofocus technique—which is also good practice with a dSRL. It may take a fraction of a second longer than the fastest of phase detection dSLRs, but it is absolutely accurate to a hair, which a dSLR is not. My D700 has 12 menu slots for fine tuning lenses for front or back focus. Not needed with either Fuji.
The camera will not think for you, nor will it read your mind. There is a clearly visible rectangle in all three viewing methods that you place on your subject. If it is off your subject, that is where it will focus. It expects you to be enough of a photographer to be able to anticipate a shot by a fraction of a second, and command it to get the shot. If you are a photographer, you will not notice any problem whatever. I was shooting in available darkness last night—all people-shots in a restaurant—and it was beautiful to use. If you need a camera that largely relieves you of photography, check out the little Nikon 1 system.