In theory, yes it should.

In practise, if the Chacho is more responsibly managed / less printed than the Peso, that 1:1 peg will make the Chacho harder to find, and its purchasing power will rise slightly over the Peso. The reverse if it is less well managed.

But mostly it should track the Peso.

My concern is more if the Chacho were to be abruptly withdrawn, in case of a Federal ban or the local government ceasing to accept it as payment of taxes and charges.