Are Americans dual nationals after they naturalize and before they relinquish?

The clock gets rolled back for the U.S. case

Whether you relinquish/lose your nationality (which is a requirement for Japanese naturalization) before the naturalization process completes or afterwards depends on the country of your original nationality.

Japan would probably prefer that you lose your nationality prior to receiving your Japanese nationality, as it is a prerequisite for receiving Japanese nationality and is easier to verify and enforce when done beforehand.

Statistically speaking, the vast majority of people who naturalize to Japanese are required to legally give up their previous nationalities prior or instantly/automatically upon receiving Japanese nationality: this vast majority being the Chinese (both PRC & ROC) and the Koreans (both ROK & DPRK). Even applicants from the G-7 country of the United Kingdom are required to lose their nationality prior to naturalizing.

If one is required to lose their nationality prior to receiving Japanese nationality, then the losing of your original nationality is the very last step of the Japanese naturalization process; they make sure all the other paperwork is cleared and approved prior to asking you to give your nationality up. Thus, there are no cases where you give up your nationality only to find you did not pass the other Japanese nationality requirements.

For other countries (such as New Zealand and the United States of America), the procedures for losing your nationality are such that you do it afterwards. The most common reason for some countries insisting on losing afterwards is because they do not want anybody becoming stateless.

Article 15 of the U.N. Declaration of Human Rights says that every human is entitled to a [one, not multiple] nationality, and there are many treaties that countries have signed on to to prevent / reduce the amount of stateless people in the world. This right was formed after World War Ⅱ, when many States simply ceased to exist, creating millions of stateless people.

Even Japan will not let its citizens become stateless; if you become Japanese then want to change your nationality, you must first acquire another nationality before they will let you renounce your Japanese nationality. This is despite Article 22 clause 2 (第２２条　第２項 {dai nijūni jō dai ni kō}) of the Japanese Constitution, which says:

(2) Freedom of all persons to move to a foreign country and to divest themselves of their nationality shall be inviolate.
②何人も、 {Nanibito mo, }外国に移住し、 {gaikoku ni ijū shi, }又は国籍を {mata wa kokuseki o}離脱する自由を {ridatsu suru jiyū o}侵されない。 {okasarenai.}

The United States is actually an outlier in that it will let its citizens renounce their citizenship and become completely stateless. The reason Japan makes Americans renounce after obtaining Japanese nationality rather than before is due to the fact that America differentiates between renouncing and relinquishing, especially with respect to taxes and ramifications. Japan allowing Americans to obtain citizenship beforehand sets up the conditions necessary for relinquishing — which has the nuance of other external factors forcing the condition rather than the desire to lose your nationality being the prime motivator.

Once Japanese citizenship is obtained, Americans are expected to divest themselves of their U.S. nationality within two (2) years or earlier — which is the same time limit that a naturally born dual-national Japanese-American gets when they become the age of majority (twenty; 20 years old) for Japan and must choose their nationality (国籍選択 {kokuseki sentaku}).

During this "limbo time", you are in reality a dual national, with two passports.

However, once the U.S. State Department processes and approves your loss of U.S. nationality paperwork, they back-date the Certificate of Loss of Nationality to the day you naturalized to Japan. This is because legally, you lose your U.S. nationality on the date that you "knowingly committed an expatriating act (in this case, naturalizing to another country) and voluntarily and formally reported the action with the intent of losing American nationality." This contorted logic and legalese is to satisfy the requirements of the U.S. Constitution's 14th amendment and the later Supreme Court rulings surrounding it.

Thus, once your CLN is approved and issued and your passport cancelled, on paper, you were never a U.S. national at the same time you were a Japanese naturalized citizen. Even though in reality, you were.

Now, clever people figured out there was a tax loophole to exploit here: one could obtain the nationality of a country by naturalizing, then when U.S. taxes (which must be declared and possibly paid no matter where you live and work in the world) became inconvenient, you could then report your relinquishing event and argue to the U.S. Internal Revenue Service that you were not in fact a U.S. national during those tax years.

The IRS has discovered and closed that tax loophole: the current U.S. tax code won't relieve you of your tax liabilities until you've actually had your relinquishment processed and approved, and you've filed your 8854 form (Initial and Annual Expatriation Statement) along with your final 1040 tax form.

The reverse for other countries where you're required to lose your nationality prior to receiving your Japanese nationality, though, is not true: the time between when you lose/renounce/relinquish your previous nationality and the time you receive your Japanese nationality you are and will be on paper — very briefly — technically stateless (無国籍 {mukokuseki}), and it will state as much on your newly minted family register (戸籍 {koseki}). They do not backdate the date of Japanese naturalization to the day you lost your other nationalities.