Yes they can. Anything reasonably calculated to lead to admissible evidence can be sought in discovery. The capacity of a corporation to sue or be sued is relevant.
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.
Articles of Incorporation are public records, so they cannot be withheld. The plaintiff can order a copy from the Secretary of State, but if the defendant is asked for a copy in a request for production, the defendant must produce. A copy of the articles should be in the defendant's possession, custody or control, and as my colleague indicated, may be relevant including with respect to capacity to be sued.
This response is provided as general information only. It is not intended to be legal advice. Legal advice must be based on the exact facts of the particular situation, and by necessity this forum is not appropriate for discussion of specific, exact facts. Contact a lawyer for more specific advice. My answer to your question on AVVO does not create an attorney-client relationship.
Yes, the plaintiff can demand production of the Articles of Incorporation through a document production demand pursuant to Code of Civil Procedure section 2031.010 et seq.
Alternatively, as Attorney Bennett indicates, you can also obtain a copy of the Articles of Incorporation directly from the Secretary of State.
Production of the Articles of Incorporation is permissible so long as this document is reasonably calculated to lead to the discovery of admissible evidence.
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.