CA has two very distinct and separate boards, actually the one that covers the LVNs is no longer called a Board, but it referred to as a Bureau and is now under the Dept of Consumer Affairs as of July 1 of this year.
Not sure which exam that you took since it was not mentioned. If the PN exam, then results are mailed out about a month after testing, and if they are busy, can be up to six weeks or so. You will not see your name on their website as the license is not paid for until you pass the exam and receive the bill in the mail and they receive payment.
For the RN exam, the average wait time can be about ten days. We have seen earlier but that is not the routine for all. CA BRN will permit a new grad to test before they have a completed file on them provided that the student's name is on a roster submitted by the school. They are unable to release the results until the file is complete and this can sometimes take up to a month. If it has been two weeks and you wrote the RN exam, then we recommend that you contact the BRN to see what is missing from your file, they will not contact you.
They are actually unable to give results over the phone in any way, shape, or form; and can be subject to losing their jobs over it. They have no idea if you are really who you state that you are, so this just makes legal sense. Whatever information it given over the phone has no legal bearing on anything.
Best of luck to you.