Does Xiaomi's regular SMS lock screen affect it?

Does not affect sending and receiving.

As long as the phone is not turned off, the settings of the phone are valid, and locking the screen does not affect its scheduled sending function.

If the mobile phone receives the information, the mobile phone will display the notification or not according to the user's settings when the screen is locked. This is determined by the user's settings and has nothing to do with the lock screen itself.