I think the Republic would resist for quite some time, but by this time the Mandalorians would have heavily outnumbered the Republic (by means of conscription) and would have many more supplies available to them. Once they hit the Core, the Republic would only delay the inevitable. I have no doubt that they would put up a good fight, but they would lose eventually.
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.