You want to get yourself a lawyer and come to court on your court date. If you fail to show up, the court will issue a warrant for your arrest. Once you're found because of the warrant, you will end up in jail for long enough for immigration to find you. Since you are illegal, that will put you in a very bad situation.
On the other hand if you attend, your immigration status is not likely to arise. And the DA may not notify immigration.
Generally a first DUi is going to result in a suspension of your license if you have one, hefty fines and some form of unsupervised probation for anywhere from 3 to 5 years, along with driving classes. There's a mandatory 48 hour jail sentence
which can be waived in favor of community service.
There is also some bargaining leeway. California allows for a plea to a "wet reckless" -- an alcohol related reckless driving charge. The advantage to that is that the penalties are lower and there is no license suspension. Such a disposition would have to be bargained for, which is one more reason to make sure you have a lawyer with you when you come to court.
If you are indigent and affording a criminal
lawyer would cause you extreme hardship, you can plead NOT GUILTY at your arraignment and ask the court to appoint you a public defense lawyer.