Does restoring a local backup using iTunes enable activation lock? Let's say I have an Apple ID that's been disabled/locked for security reasons.

This account is linked to my iPhone and in order to remove it or to simply disable find my iPhone, I have to answer the security questions on the account which I don't remember anymore. So basically the account is glued to the device with FMI enabled.
So then I get a new phone and restore a local iTunes backup that I made of the old phone with the account issue on to the new phone.

FMI shows as enabled on the new phone's settings but I am not sure it's actually enabled. IMEI checker sites such as imeipro show that it's disabled but I want to get your opinion on the matter. I want to format the new phone and worry it too will become activation locked.
Does restoring a local backup using iTunes enable activation lock?
No, restoring a backup from a device that is locked doesn't lock the new device - devices are locked to accounts, not files in the backup.
Each device can be tied to find my and data can move between accounts without changing the status of iCloud / Activation / MDM or other locks.