Special Marriage Act?

Hi, I am 30 years old and the girl I want to marry is 23 years old. We both are Hindu and belong to the same caste. Our parents had agreed to our marriage 2 years back. Now, for some reason, they have quarreled and have broken the marriage agreement and keeping us separate. But in these 2 years, we have fallen in love very much and want to go for registered marriage under Special Marriage Act. The girl is still in her parents house and myself with my parents. So, we apply for marriage under special marriage act, is there any chances that our parents come to know about this (like is there any notice sent to our address?). We have decided to marry first and then bring it to our parents notice, so that they have to agree for our marriage. Please help.