Could a large constrictor kill a small animal?
Constrictors doesn't have uniform body circumference from head to tail. They coil around the prey accordingly. In your example, if the prey is very small, it just swallows. If its little big, it coils a little bit (check some videos like this) say two turn coil. This will only cover top half feet of constrictor's length which is of lesser diameter than the body. 

So basically, they crush the prey and perform a kill. Its not a necessity for any constrictor to use its entire body to coil around a prey. They adjust their coil level to control the prey.