Nope. Suppose that say, state #16 and state #416 are in fact identical. Well then this machine does not halt, as of course being in this state leads back to the same state again in just four hundred moves, state #17 and #417 and so on will be the same too.

The notional paper tape might have identical states, but if this happens in a machine that does eventually halt the rest of the machine state must be different, and these are both state that a universe must keep in order to instantiate the machine.