The problem would be explaining it
But if they can, then they could do anything
The only thing I can think of that the Juubi is Kaguya's would be that Isshiki intends to resurrect her so he can do whatever he needs doing to her. So revenge route? Or just taking her back to be arrested.
But the problem is that if he can collect the Juubi and store it in a different dimension, that means he has the means to take the Gedo Mazou from the moon as well. The only person that can stop him from doing that is Toneri. So I would say that he probably has no idea that the moon is now empty and being guarded by puppets only.
So the only excuse that I can think of as to why he hasn't stolen the Gedo Mazou yet is because he has no idea of the current situation of the moon. He probably still thinks that the moon are filled people upholding Hamura's decree instead of just one person playing with puppets.
So everything does point out to the Juubi being that dimension's chakra. As for the vessel of that Juubi, perhaps he took it in for himself? That would explain how he was creating bodies that can tolerate his Karma.