The short answer is yes. Ben Price is not an official officer of the law. Banks employed private detective agencies, such as the famous Pinkerton's, for security in O. Henry's time. Ben Price was not legally obligated to arrest Jimmy Valentine for the three safecracking jobs Jimmy had committed in Indiana right after being released from prison. As a matter of fact, Ben Price did not know for sure that Jimmy was the perpetrator. He was not like Jimmy Wells in O. Henry's story "After Twenty Years," who was a sworn officer of the law and legally and morally obligated to arrest his old friend Bob, or at least to have him arrested. Sherlock Holmes was also a private detective and not legally obligated to arrest criminals. In some stories he let offenders go free because (1) he felt some compassion, and (2) he felt sure the offender was not going to commit any crimes in the future. This was the case, for example, in "The Adventure of the Blue Carbuncle." The thief named Ryder begs for mercy. Holmes thinks it over, then:
"Get out!” said he.
“What, sir! Oh, Heaven bless you!”
“No more words. Get out!”
And no more words were needed. There was a rush, a clatter upon the stairs, the bang of a door, and the crisp rattle of running footfalls from the street.
“After all, Watson,” said Holmes, reaching up his hand for his clay pipe, “I am not retained by the police to supply their deficiencies."
I myself would perhaps be even more inclined than Ben Price to allow Ralph Spencer to continue living the life of a small-town businessman under an assumed name, because I have shared Jimmy Valentine's experiences vicariously and feel certain that he deserves to get a break. Jimmy will be a good family man and a good citizen from now on. He will be much more of an asset to society living a staid, conventional life than living behind prison bars.