No, the responding party's failure to respond to discovery has no effect on the discovery cut off. Moreover, if the initial trial date is continued, the discovery cut off is not automatically extended.
If the responding party does not provide any responses, you would need to make a motion to compel noticed for hearing 15 days prior to the discovery cut off.
California Code of Civil Procedure section 2024.020 provides:
"(a) Except as otherwise provided in this chapter, any party shall be entitled as a matter of right to complete discovery proceedings on or before the 30th day, and to have motions concerning discovery heard on or before the 15th day, before the date initially set for the trial of the action. (b) Except as provided in Section 2024.050, a continuance or postponement of the trial date does not operate to reopen discovery proceedings."
Therefore, if the initial trial date is continued and you wish to conduct additional discovery, you will need to make a motion to reopen discovery pursuant to California Code of Civil Procedure Section 2024.050, which provides:
"(a) On motion of any party, the court may grant leave to complete discovery proceedings, or to have a motion concerning discovery heard, closer to the initial trial date, or to reopen discovery after a new trial date has been set. This motion shall be accompanied by a meet and confer declaration under Section 2016.040. (b) In exercising its discretion to grant or deny this motion, the court shall take into consideration any matter relevant to the leave requested, including, but not limited to, the following: (1) The necessity and the reasons for the discovery. (2) The diligence or lack of diligence of the party seeking the discovery or the hearing of a discovery motion, and the reasons that the discovery was not completed or that the discovery motion was not heard earlier. (3) Any likelihood that permitting the discovery or hearing the discovery motion will prevent the case from going to trial on the date set, or otherwise interfere with the trial calendar, or result in prejudice to any other party. (4) The length of time that has elapsed between any date previously set, and the date presently set, for the trial of the action. (c) The court shall impose a monetary sanction under Chapter 7 (commencing with Section 2023.010) against any party, person, or attorney who unsuccessfully makes or opposes a motion to extend or to reopen discovery, unless it finds that the one subject to the sanction acted with substantial justification or that other circumstances make the imposition of the sanction unjust."
The information presented here is general in nature and is not intended, nor should be construed, as legal advice. This posting does not create any attorney-client relationship with the author (who is only admitted to practice law in the State of California). For specific advice about your particular situation, consult your own attorney.
There is nothing which one can add to Mr. Chen's answer, correct analysis and law.
The above is general legal and business analysis. It is not "legal advise" but analysis, and different lawyers may analyse this matter differently, especially if there are additional facts not reflected in the question. I am not your attorney until retained by a written retainer agreement signed by both of us. I am only licensed in California. See also avvo.com terms and conditions item 9, incorporated as if it was reprinted here.