YES; if all the requirements of Rule 7, Arizona Rules of Family Law Procedure ("ARFLP") are met.
The purpose of the rule is to provide protection to litigants and children subjected to domestic violence. Therefore, any qualifying party may file or respond to a family law proceeding without disclosing his/her address once the court has approved the action and ordered an address protected.
To obtain approval, any person filing an initial or post-judgment petition, motion or response, whose address is not known to the other party and who reasonably believes that physical or emotional harm may result to the person or a minor child if the person's address is not protected from disclosure, may request the court to designate that party's address as protected by:
filing the substantive petition, motion or response thereto with no address included on it;
filing a written request using the Request for Protected Address Form;
lodging a proposed form of order with the court, ordering that the address be protected, except that if there is a valid Order of Protection and the clerk can verify the existence of the Order of Protection, address confidentiality shall be automatic upon filing a written request; and
filing the party's address on a separate sheet of paper for court use. If the court orders that the address shall be protected, the clerk of the court shall thereafter protect the person's address from public disclosure until the court orders otherwise. A person whose address is protected from disclosure under this rule may be served with all subsequently filed documents, by regular first-class mail at the address provided to the clerk. If the court does not order that the party's address is protected, all subsequent filings must include the party's address.
Next, within five (5) days of the filing of a request for an address to be protected, the court shall rule on the request, ex parte, without a hearing, unless the court finds it appropriate to set the request for hearing. If the court sets the request for hearing, all parties who have appeared shall be notified of the hearing, and the hearing shall be held within twenty (20) days of the filing of the request.
At any time during the proceedings, the court may order that any protected address no longer be protected upon request of the party whose address is protected or after a hearing and upon a finding that there is no reasonable belief that physical or emotional harm may result to the person with the protected address or to a minor child.
If your address is ultimately ordered protected, then you should be aware that there remains a continuing duty to provide the clerk of court with a current and correct mailing address where you can be served with process.