:salamext:
As long as the conditions of nikah are met marriage is valid. However, I'm not going to get into the ins and outs of the conditions of marriage because a nikah that is done 'privately' sounds very fishy. Marriage (nikah and waleema) is a time for celebration and happiness and it is a time where you need the sincere and heartfelt duas of your friends and family. Zina is kept quiet and secret but marriage, by its very nature, is not.