The Roman Empire would have prospered longer had Nero and Caligula not been successive emperors. These two individuals were some of the most bloody, horrific leaders in history. It definitely put a permanent stain on the history of the Roman Empire. It would have lasted perhaps hundreds of years longer without these men in power.
When you look at empires and their governments as corporations, it becomes a lot easier to figure out how much leadership counts. The Roman Empire simply did not have a lot of time left after being subject to the whims of two Emperors who never should have been in the executive suite.
Nero and Caligula were brutal and power hungry. I'm not sure which one was worse, but they were both extremely detrimental to the Roman Empire. The thought that they weakened the empire so much that they were eventually overrun by Germanic tribes boggles the mind. This would be like Somalia defeating the US.
Rome culturally supported slavery and the establishment of a decadent elite . History will show, that this kind of system has always failed. It breeds animosity amongst the people. A country could never continue to prosper if only a small portion of it's people are allowed to enjoy it's prosperity.
No, they would not have prospered longer even if these two not so great leaders had been at the throne back to back. Problems in this empire had been building up for a long time, and one or two leaders could not have a significant impact on the entire empire.