Yes, transit and anchoring are generally allowed. A few areas may restrict or prohibit transit and anchoring to protect a particularly vulnerable habitat or species, though all have allowances for anchoring or transit in emergencies. The relevant language is found in the California Code of Regulations, Title 14, Section 632, subsections 632(a)(7) and 632(a)(8), which state the following: 

(7) Anchoring. Vessels shall be allowed to anchor in any marine protected area or marine managed area with catch onboard unless otherwise specified in subsection 632(b)(opens in new tab), areas and special regulations for use. Fishing gear shall not be deployed in the water while anchored in a state marine reserve. Fishing gear, except legal fishing gear used to take species identified as allowed for take in subsection 632(b), shall not be deployed in the water while anchored in a state marine recreational management area, state marine park or state marine conservation area. Anchoring regulations shall be consistent with federal law and allowances made for anchoring required by emergency or severe weather. 

(8) Transit or Drifting. 

• (A) Vessels shall be allowed to transit through MPAs and marine managed areas (MMAs) with catch onboard. Fishing gear shall not be deployed in the water while transiting through a state marine reserve. Fishing gear, except legal fishing gear used to take species identified as allowed for take in subsection 632(b), shall not be deployed in the water while transiting through a state marine recreational management area, state marine park or state marine conservation area. 
• (B) Spearfishermen with or without catch shall be allowed to transit through MPAs and MMAs. While transiting MPAs and MMAs that prohibit spearfishing or while in possession of species not identified as allowed for take in the MPA or MMA being transited, spearfishing gear shall be in an unloaded condition, not carried in hand, and the diver shall remain at the surface. 

Special closures may restrict or prohibit transit, with or without catch on board. Check the individual special closure regulations for details.