Check with the clerk about what documents you will need. People who are here unalwfully get married every day, and going through that process should not lead to the initiation of removal proceedings.
Whether you will be able to remain in the country will not depend on the court clerk, but on the decisions and actions of USCIS and/or ICE.
The issuance of a marriage license should not depend on immigration status.
J Charles Ferrari Eng & Nishimura 213.622.2255 The statement above is general in nature and does not constitute legal advice, as not all the facts are known. You should retain an attorney to review all the facts specific to your case in order to receive advise specific to your case. The statement above does not create an attorney/client relationship. Answers on Avvo can only be general ones, as specific answers would require knowledge of all the facts. As such, they may or may not apply to the question.