In the long run it was not, unless you are claiming that the republican senate would have been able to handle the Migration Period any better.
After all, I think that people are pretty confused when they think of this idea of the "decline of Rome." I don't even know what that means. The Germanic peoples who settled into Roman territories had become so Roman, in culture, language, institutions, etc, that it's hard to see how they are different.
Are you talking about what a map would show as Rome's borders? In that case, what lead to Rome's decline is the settlement of the migrating tribes and the usage of them as mercenaries that was bad in the long run.
Institutions, in my opinion, had nothing to do with the "decline of Rome." It has 100% to do with how they handled the migrations and the decisions they made about their military.