Can a corroded battery wire cause a check engine light on?

Well, yes and no, it depends. Many of the sensors on modern vehicles use voltage as a control. If the sensors detect lower than expected voltage due to poor electrical connections, that could cause a check engine light. However, once the car has been started and is running, most (if not all) voltage is supplied directly by the alternator and not the battery.

(https://www.quora.com/Can-a-bad-battery-connection-cause-a-check-engine-light-What-problems-can-corroded-battery-terminals-cause)