yes, your chances will be lower, but not impossible.
most gov't schools use cantonese (it being the mother tongue of 95% of the population), the others use English. i don't know of any that use mandarin (not that they don't exist. they might, i've just not heard of them.)
there is a local school in sai kung, called LEE SIU YAM MEMORIAL PRIMARY SCHOOL. they have an english stream and a cantonese stream. my son attends in the chinese stream. while not perfect, we are quite happy with the school. i'm not fussed about the english as he gets that at home, but i am very glad he's learning the cantonese reading and writing as well as speaking.
the staff is very friendly and helpful. you may want to give them a call. they don't start the year until sept 3... so you won't be missing as much as with an int'l school, which start this week and next.