yes,st.Anthonys chembur may be maharastra govt aided school because it follows state syllabus...but this school is not mentioned in the list of Christian schools that you listed above posts....
In India all CBSE/ICSC schools,except kendriya vidhalaya,jawahar navodhaya,navy schools ,comes under private management..where teaching salaries are not given by the government,its the duty of the respective management..that are not government staffs either...
There are many Christians schools follows state syllabus(like Kerala state syllabus.),where salaries are given by state government,they are known as government aided Christian schools..Majority of state schools in Kerala are these types...