Did Roman Emperors of the second century with their message of Pax Romana represent the interests of the Romans?
This is a good question. The idea of pax Romana started with Augustus. Sometimes it is even called pax Augusta. It roughly started with Octavian's victory over Antony at the battle of Actium in 31 BC and this pax Romana continued to the second century - perhaps ending with Commodus. This was certainly a time of prosperity and consolidation, and all of these things were supposed to serve the interest of Rome. The message of peace can be seen a "soft power," that is, ideology that would get people and nations to side with you. Who does not want peace?
With that said, a more sophisticated answer is necessary, because what came after the second century was the vast and many troubles of the third century. In other words, decline settled in. The seed of decline, then, was sown during the second century.
In the third century, there was hyper-inflation and Diocletian had to even issue a price edict. There were succession problems, and there was always Germanic threats to the North. From this perspective, we can say that the pax romana was always for the good of Rome by intention, but unwittingly the Empire could have gotten weaker without further military conquests.