To cut and run means to leave a situation or arrangement as soon as things go awry, which is what the speaker expected him to do when he found out about the personal baggage.
Consider the statement "I backed away, expecting him to flee the scene very quickly, now that he knew I had some kind of personal baggage.". Is the statement "I backed away, expecting him to cut and run, now that he knew I had some kind of personal baggage." false? Yes/no/unknown