It is entirely possible that the California government will give you a CA state ID without arresting you. They may also choose to arrest you and try to send you back to Texas.
The best thing to do is take care of the Texas warrant. You will not be able to get a California driver's license with that not being dealt with. Getting an CA ID may be possible.
Why not call the Texas court & see if you can pay it by mail. It would be a lot easier than worrying about when you will eventually be arrested.