It could happen that way with zigbee, but not with Zwave. Z wave doesn’t do a real time update of the method of pairing. So if you add the zwave device originally while on power, the hub continues to think it’s on power even if it switches over to battery. Z wave devices don’t re-join the network the way zigbee devices do. They just join once and belong to that network until they are excluded.
Now if the zwave device switches over to battery it may refuse to repeat any messages in order to preserve its battery life, so the messages can get lost. But if joined as a mains powered device the hub will continue to think it’s a Mains Powered Device, so that’s not going to be the issue in this case.