It can depend on whether the Sheikah Slate is present or not. The Master Cycle Zero is summoned upon use of the Sheikah Slate, so if the Sheikah Slate is not present, the Master Cycle Zero may not be.
BUT...
Just as how the Sheikah Slate may be replaced, the Master Cycle Zero might be replaced too. In other words,we might get a new vehicle for doing what the Master Cycle Zero can do, even if a different vehicle.