As has been stated above, most MANPADS are designed to bring down relatively small aircraft. Large, commercial aircraft are designed with multiple redundancy, and are supposed to be able survive such catastrophic events are engine rotor disk failures. So it isn't actually unreasonable to assume that a single hit on a single engine would be survivable in many cases.
Therefore the answer to the question posed by the thread title is "yes, it might indeed survive".
Obviously there are circumstances under which it would not, just as there are circumstances occassioned by other than hostile action which would be catastrophic also.
Obviously there are things both the 'bad guys' and the 'good guys' can do to skew the odds. These are not, however, really a good idea for an open discussion; I assume that the 'good guys' are already doing some of those things.