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.
I don't think the people of the Core Worlds are exactly recruitable... have you played Alderaan? Those pompous nobles would never become Mandalorian. Most likely their would be resistance on every world, and lets face it. The option in which the Jedi never intervene is impossible. I mean, when they finally reach Coruscant the Jedi Council aren't just going to meditate and let the Mandorians shoot them in their chamber :P
Sure the Republic would be heavily, heavily outnumbered. But I believe the Mandalorians would fall apart, fighting amongst themselves for the galaxy they have pillaged and wipe each other out - this would make the Republic's job a lot easier.