Eventually, the third Muhammad, Maometh, combines Islam with Buddhism to create the zensunni faith.
Jokes aside, its hard to say. Christianity didn't do well early on and had a much harder time of weathering the storm of oppression than Buddhism did. Like China, Japan is a country where religion very much adapts to the people to survive, and the practices of the hidden Christians was such that we can see Buddhist influences in its isolation.
Now Islam has certainly proved adaptable too (contrary to popular belief), but I see two challenges with it being sustained in meaningful numbers.
1) Japans religions arguably jelled better with Christianity. The complexity of Christ's nature as a god and man was very familiar to Japan which had told stories from Hindu mythology for generations. His descending down to hell, suffering to liberate others is also very understandable from the perspective of Mahayana Buddhism in which the Bodhisattva's were claimed to do similar things. Not only is the nature of Christ very different in Islam, but Muhammad as a "character" doesn't have as good a link to Japanese culture (that I am aware of anyway).
Also, Christianity in Japan merged with Shinto very well, allowing Japanese Christians to worship the emperor and Christ, something a lot harder to justify with Islam.
2) Japan largely adopted religion as it became endorsed by local powers. Buddhism went from persecution to very popular with links to China. Christianity did so with links to western powers. Islam would need a great power that has regular interactions with Japan for the Shoguns to be more tolerating of it.