Yes, you can make Emergency calls when Screentime is enabled on Android device. Please make sure to add your contacts to the Emergency info section, so that your child can use lock screen Emergency Dialer to make calls.
Open Android settings app > search for Emergency information (Users > Emergency Information) and you will see two tabs - one for information and one for contacts. Select the contacts tab and add the contacts there.
NOTE: Some device manufacturers may not support this option. Please check with the specific manufacturer support for further assistance.