Deceased had only a notarized appointment for an Executor of Estate but no will; is it considered she "died intestate?
If the decedent died without a will, then the decedent died "intestate". However, the appointment could be used as evidence to appoint the person named as Administrator of the probate estate.
A person dies intestate when they die without a valid will. A notarized appointment of an executor of the estate is not a valid will, unless it also complies with California law regarding attestation of wills, or is entirely holographic.
You should retain a qualified attorney to answer this and other questions regarding the estate.