I would disagree. The Mandalorians aren't even a nation - they are a nomadic, barbaric tribe who's culture revolves around war. I can't see them keeping hold of the Core Worlds which would need government and policing - I mean do you think the Mandalorians would be equipped to deal with the Cold War uprising on Coreilla? Even the Empire couldn't handle that. I believe as the war begins to peter out, and the Mandalorians begin encroaching on the core worlds, they would begin to fall apart, fighting each other and fighting insurgencies. And the Republic would eal the killing blow. Ultimately they could not govern a galaxy.
The Mandalorians have never governed anything they conquered, really. They go in, kill any resistance and recruit the survivors. If they didn't do this, they wouldn't be able to maintain the war effort. They wouldn't even have been able to go to war if they didn't recruit people. The Mandalorian clans had taken a huge hit after the Exar Kun debacle, so they had to recruit in order to effectively maintain the war effort.
They have never been about conquering. They would take over a planet, take what they want and leave. And if they can't take what they want, they bombard the planet. Look at Serocco. They devastated the planet. If the Corellia uprising happened to the Mandalorians, they would have bombarded the planet.
And I don't think the Republic would be able to retake the Core worlds as effectively as you think. By this time, the Mandalorians would have utterly outnumbered the Republic forces and have the Core Worlds surrounded, slowly moving inward. Once the Mandalorians hit the Core, the Republic would be doomed without the Jedi.