Hard to say, but after law school, if you wish to become a member of the bar, you will need to go through the character & fitness review. This will likely involve a through review of your background, at this point they will likely be aware of what schools you have enrolled in. It may well be a very uncomfortable moment if there is a discrepancy with what was stated with what one put onto their law school applications.
Also keep in mind that there are several data points which are cross checked by schools, so it within the realm of possibility that a lack of information may be detected. Even if it is a small chance, it is not worth the downside risk.