Generally yes. However, if the violation is only for failure to display registration then the arrest must be very limited in time and scope, with the primary focus being upon the officer providing the driver with the "notice to appear" set forth in California Vehicle Code section 40500, which has been described and interpreted at length by various California courts administering traffic laws.
First, "California has numerous statutes governing the issuance and renewal of drivers' licenses, ID cards and vehicle registrations. In resolving the issues involved in this case we cannot focus on any single statute or phrase, but must consider the entire statutory scheme." Lauderbach v. Zolin (1995) 35 Cal.App.4th 578, 583.
Second, the Vehicle Code primarily applies to vehicle infractions, and the penal code applies to criminal infractions. They are separate codes, and generally remain separate unless it is necessary or appropriate to read them together (i.e., when the Vehicle Code directs us to use the Penal Code). The authority for the traditional arrest is found in the Penal Code (see e.g., PC 836), while the authority for the limited arrest "notice to appear" is found in the Vehicle Code. Courts have discussed their distinction and application with regard to the facts on the road and in the courtroom. A very helpful case to assist with understanding how to analyze this topic is People v. Battle(1975) 50 Cal.App. 3, Supp 1 ("we must conclude that it was not the intent of the Legislature to enact inconsistent statutes and, further, that when it added the term 'public offense' to section 16 it was not so categorizing infractions because if it did so, it would have caused inconsistency between sections 19c and 689 of the Penal Code."). Also note for context purposes, Per Vehicle Code section 40302, persons who would otherwise be cited and released for a Vehicle Code infraction or misdemeanor may be arrested and taken immediately before a magistrate when the person fails to present his driver's license or other satisfactory evidence of his identity for examination. The arresting officer has the discretion to determine what constitutes "other satisfactory evidence of his identity," when the subject fails to provide a driver's license. See e.g., People v. Monroe (1993) 12 Cal.App.4th 1174, 1182; People v. McKay (2002) 27 Cal.4th 601, 619-625. Note also though that with regard to unlicensed drivers, according to California Vehicle Code section 12801.5(e), "Notwithstanding California Vehicle Code Section 40300 or any other provision of law, a peace officer may not detain or arrest a person solely on the belief that the person is an unlicensed driver, unless the officer has reasonable cause to believe the person is under the age of 15 years." See also, California Penal Code section 853.5.
Third, the general consensus of law enforcement officials and attorney generals across the country is that peace officers may arrest an individual for most vehicle violations (including misdemeanors and infractions) committed in their presence. See, California Vehicle Code section 40300 ("The provisions of this chapter shall govern all peace officers in making arrests for violations of this code without a warrant for offenses committed in their presence, but the procedure prescribed herein shall not otherwise be exclusive of any other method prescribed by law for the arrest and prosecution of a person for an offense of like grade.") There appears to be a sliding scale, and definitions of the particular State statute in questiton are important. For example, in the case of a toll violation in California (where cameras record vehicles, and violators are sent letters) an arrest is not appropriate (presumably because it would be duplicative of the camera + letter procedure). See
CVC 23302.5 ("A violation of subdivision (a) is subject to civil penalties and is neither an infraction nor a public offense, as defined in Section 15 of the Penal Code. The enforcement of those civil penalties shall be governed by the civil administrative procedures set forth in Article 4 (commencing with Section 40250) of Chapter 1 of Division 17.")
Lastly, when words are parsed or doctrines are summarized with sound-bites, it is possible to manufacture theories that a person cannot be even briefly detained for a minor traffic offense. However, such an odd rule would require officers to simply let the law go uneforced (thereby abandoning their affirmative duties to enforce laws), or alternatively to put a tail on the anonymous (unregistered) violator and follow them to their destination to hopefully gather evidence of their identity. It seems like that would be silly and unproductive, and we know that the law does not require silliness or bad police work. It requires due process - and the 'notice to appear' procedure set forth above comports with due process because it (a) helps enforce the law, and (b) is the most minimal intrusion on liberty possible given the circumstances because the stop is so brief and amounts to basically a polite exchange of paperwork. For legal citations, please see my related legal guide: Is There An Absolute Right To Travel In A Car On Public Roads - https://www.avvo.com/legal-guides/ugc/is-there-an-absolute-right-to-travel-in-a-car-on-public-roads