Sorry that this took quite a bit longer than I usually take. I had to do squeeze some research on this (and the mood to do the writeup) in between my research, which took some time.

Although this is certainly only my field insofar its about Japan, I did feel like taking a look into it, because the very notion of the emperor converting to Islam (or Christianity, for that matter), is somewhere between hilarious and absurd.

Anyway, the short version is: if you mean the conversion of Japan to Islam, then, no, of course this is nonsense. But there is a reason as for why this idea even exists.

Let me quickly reiterate the relevant statement from Wikipedia:

In 1906, widespread campaigns were aimed at Muslim nations with journals reporting that a Congress of religions was to be held in Japan where the Japanese would seriously consider adopting Islam as the national religion and that the Emperor was at the point of becoming a Muslim.

The article referenced in this specific sentence clearly speaks of propaganda (and I doubt this could be misunderstood had whoever wrote this on Wikipedia not replaced the word with "campaigns"):

. . .in 1906, that the Japanese first initiated a great wave of Muslim propaganda consciously directed toward the entire islamic world. In the spring and summer of that year widespread reports appeared in Muslim journals of India, Persia, Russia, Turkey, Egypt and other countries stating that a Congress of Religions was shortly to be held in Tokyo; that at that Congress the Japanese would seriously consider adopting Islam as their national religion; and that the Emperor was on the point of becoming a Muslim. It was significant that this wave of propaganda, followed in subsequent years by comparable waves, occurred shortly after Japan's victory over Russia in 1905. Japan had been raised as a result to the status of a world power and had become potential leader of the peoples of Asia in their struggle for equality. (Bodde 1946: 311)

It is quite clear that we have to see Japan’s spreading of false information—"fake news," I suppose, in the language of 2020—concerning their affinity towards Islam within a broader political context. For one, as a means to appeal to Muslims in China, as Bodde writes two paragraphs earlier on the same page:

It is not surprising that the Japanese turned their attention early to the Muslims in China as a promising instrument for Japanese expansion. Religiously, racially, and to some extent socially the Chinese Muslims have felt themselves apart from the great bulk of non-Muslim Chinese; and they form an important minority or even a majority in certain areas which held particular strategic significance for the Japanese always fearful of Russia. Furthermore, the cohesiveness of the Muslims and their aggressiveness would have made them more satisfactory tools, in the view of the Japanese, than, for example, the numerically far greater Chinese Buddhists. (Bodde: 311)

Such a propaganda move was also intended to evoke general support for Japan within the Muslim world in general, which were to be seen as tendentially antagonistic towards the European colonial powers. It is quite noteworthy that Japan's propaganda started shortly after the Russo-Japanese-War, which saw a non-Christian Asian nation to defeat one of the—Christian—Western powers (with Japan's victory, arguably, henceforth, also Japan’s rivals on the world stage).

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Apparently, the Japanese didn’t come up with these “fake news” in limbo:

According to Akiba Jun (2013), the idea of spreading Islam in Japan had already been part of Ottoman policy in 1889/90, although these policies were never implemented. Akiba argues that these early plans, this focusing on Japan by the Ottomans, was part of Sultan Abdülhamid II’s pan-Islamic propaganda, which was actually targeted at the Muslims in India and Southeast Asia. Albeit these plans never came to fruition, this positioned the topic of Japan within Islamist discourse, and the idea of *having the Tenno be declared Calif, and therefore leader of all Muslims—under the hypothetical precondition that Japan converted to Islam—*emerged during, and after its victory in the Russo-Japanese War in the writings of Muslim intellectuals.

The rise of Japan, as it manifested in the public image through its victories first in the Sino-Japanese War, and then in the Russo-Japanese War, was “a destabilizing factor that attracted Muslim activists who wanted to cooperate. . . against the Western empires” (Esenbel 2011: 1). The Japanese victory was celebrated in newspapers, and recontextualized from the conflict between two nations to the conflict between the “downtrodden East” and the “imperialist West.” Japan’s modernization was perceived as a model by Ottoman intellectuals such as Mehmed Akif and Abdullah Cevdet, who saw Japan and its Meiji constitution as proof that there was, indeed, a path to become a modern nation state without renouncing one’s own traditions entirely. But also Pan-Islamist intellectuals in Egypt (e.g., Mustafa Kamil and Ahmad Dafzli) utilized Japan’s rise to power in their own anti-British national discourse (Esenbel: 4).

At the same time, Japanese military and civilian elites with an Asianist agenda advocated for closer ties to the Islamic world: for example, Hasan Harano Uno, a Japanese Pan-Asianist who had adopted a Muslim name, argued “that Japan and the Ottomans could prevent European imperialist activities in Asia” (Esenbel: 6).

As you can see is that the “backdrop” of Japan’s employment of propaganda targeted at Muslim audiences has a history: the propaganda wave of 1906 (which was not the last policy targeted at the Islamic World, as both Bodde and Esenbel show) directly reacted to a positive climate within Muslim intellectuals as a result of the Russo-Japanese War. Nevertheless, both sides apparently had different agendas: these events occurred within larger discourses of (Pan-)Islamism and (Pan-)Asianism, and, as Esenbel (18) concludes:

Although Japanese Pan-Asianism and political Islam shared a critique of the West that helped create dialogue between them, in the end, Japan’s use of Islam represents the same process as that of contemporary Western powers: linking intelligence strategies and cultural studies so that knowledge serves the interests of world power.

Hope there still was interest in this, else I wasted a loot of time learning something new only for myself (huarhuar).

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(final note: I inserted some names to make further investigation into the subject easier)

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References Cited

Akiba Jun. “Ertuğrul Fırkateyni ile Japonya'ya Ulema Gönderme Girişimi [Erutūruru-gō ni yori Nihon e no uramā haken no kokoromi]." In Nihon chūtō gakkai nenpō 29:1 (2013), pg. 129–143. Available here. Note that this paper is written in Turkish, with a short English abstract and a bit more detailed Japanese summary (the latter two I can read, the main text I cannot).

Bodde, Derk. “Japan and the Muslims of China.” In Far Eastern Survey, 15:20 (Oct 1946), 311–313, available on JSTOR.

Esenbel, Selçuk. “Japan's Global Claim to Asia and the World of Islam: Transnational Nationalism and World Power, 1900–1945,” in Japan, Turkey, and the World of Islam: The Writings of Selçuk Esenbel, Kent: Global Oriental, 2011, 1–27. Originally published in The American Historical Review 109:4 (October 2004), 1140–1170.