No. Justice by definition entails commensurate treatment. Otherwise justice cannot exist. For example, either stealing a stick of bubble gum is exactly as evil as committing mass murder, or it is not. But on no credible idea of justice can they be equal. So anyone who treats them as equal is unjust. Treating both with an infinite punishment treats them as equal and is therefore unjust. Since this analysis will show that there is always some greater evil than any specific evil, the only evil that is commensurate with an infinite punishment is an infinite evil. Humans, as finite beings, can never commit an infinite evil.
Moreover, justice itself has no value if it causes more harm than good. If justice caused more harm than good, then justice itself would be evil. Infinite punishment causes infinitely more harm than good, since the amount of suffering that results is always greater (in fact, infinitely greater) than the suffering caused by the original crime. Therefore, infinite punishment can never be a component of any system of justice that was not itself evil.
Finally, by definition, any moral being would prefer and maintain a system of justice that does more good than another system of justice. A system of justice that reforms the punished and then allows them to repurchase their freedom and happiness by achieving restitution to (and forgiveness from) all those they wronged, would produce infinitely more good than a system of justice in which punishments were infinite. Therefore, no moral being would allow any system infinite punishment--if they can create and maintain a better one, as any god could.