I believe it does...but like in the rest of life, sometimes the answers are not that easily discerned, so I'll try again.
If you mean "heavier punishments," strictly in regards to legislation, sentencing guidelines, mandatory counseling, etc. no it will not work.
If, "heavier punishment," is viewed in a less restricted scope and includes public, private, familial etc. condemnation of the behavior, exclusion from the community, abandonment by general society until such time the offending behaviors are modified, then yes it will. This, however, can only be achieved if the society at large can come to a general agreement regarding some basic moral absolutes and the individuals within that society assume a degree of responsibility for trying to live according to those moral precepts instead of lionizing those who defy them.
In what is perhaps the last intelligent thing ever written by a Democrat, Daniel Moynihan examined Durkheim's Constant in light of American social trends at the time (1993). Bork, in Slouching toward Gomorrah, expands further on Moynihan's piece and discusses it further in the context of liberal jurisprudenc.
Throwing that "if" in there makes your point work, sure. That is the only way your point works. But that is the social/cultural solution which I addressed in my last post. (which I know you couldn't have seen before you replied to me) The context I was asking the question in was taken from the article and referred solely to the government solution of criminal liabilities and I specified "heavy punitive actions" so I wasn't even ruling out less harsh legal consequences than are currently imposed.
What you originally posted is wisdom. There will never be a utopia where there is no suffering but suffering can be greatly reduced by the means suggested there. As that quote was originally intended to say it is quite true that our free republic with its liberties can't be maintained without a good measure of moral restraint in the populace.