The answer to this question is, unfortunately, not clear. While I believe the answer should be “yes” it is qualified by a somewhat complicated analysis and may depend upon the specific facts of the case.
The general rule is that, under Family Code 210 the Civil Discovery Act applies to proceedings under the Family Code. There is no statute anywhere, nor any published case under California law that prevents a party from conducting discovery in a proceeding under the DVPA (Domestic Violence Prevention Act). Since the DVPA is part of the family code, this seems like a simple analysis. (thanks and credit is given to the Sonoma Superior Court for some of the reasoning found here)
Problems have arisen in some case because of a 2005 decision in First District of California Thomas v. Quintero 126 Cal.App.4th 635 in which attorneys have argued that the court held that discovery is not permitted in Civil Harassment Proceedings under CCP 527.6. Attorneys have reasoned, by analogy, that the civil harassment scheme is the same truncated proceeding under the DVPA and that therefore no discovery is permitted in DVPA cases.
I believe that Thomas is wrongly construed. The case does not stand for a blanket rule constraining the court from using powers granted to it to prevent a party accused of Civil Harassment from effectively defending itself in such a proceeding. In Thomas the appellate court was attempting to determine whether an “anti-slapp” motion could be filed in a case involving civil harassment. A landlord filed a restraining order against a tenant who was distributing leaflets and appearing at the church of the landlord. The tenant filed an “anti-slapp” motion (strategic lawsuit against public participation) alleging that the restraining order was used to chill his free speech. The court found in favor of the tenant, reasoning that the such a motion could be filed. I believe the court simply was pointing out that temporary orders were not subject to the Civil Discovery Act and the deadlines under the Act made them inapplicable anyway. That case was not set for trial, but instead had a short hearing where some testimony was taken.
However, even assuming Quintero was being read this way, proceedings under the DVPA that involve custody of children are easily distinguishable. Under Family Code 3044, a presumption of sole legal and physical custody against a party whom a domestic violence restraining order is granted is automatically created, shifting the burden of proof to that same party to prove they should have custody. This is a very serious issue of due process, and to grant such relief against a party without that party having the right to conduct discovery seems patently unfair.
Also, if there is already a custody proceeding in place, then discovery can and should be allowed on that basis, whether or not a restraining order exists. To hold that a party cannot conduct discovery on issues of custody because a restraining order exists is an implausible argument that no court should feel comfortable accepting.
Even in proceedings without children, the quick deadlines usually created during these proceedings make it so that not much discovery is going to happen anyway without the court allowing it. Since discovery closes 30 days before trial, once a trial date is set, there is not going to be much ability to conduct discovery anyway, unless the court wishes to grant a continuance or reopen discovery, which it can do upon request.
Some legitimate concerns arise regarding discovery abuse. A party who is intimidated by another party might not want to face that party in a deposition. In that case, the court can allow the deposition and insist the restrained party not be present, or be present via video, or some other measure. The courts have broad discretion in granting or denying discovery, and although there is no published decision on this issue, the Civil Discovery Act already contains considerable authority for the court to control the process.