My understanding of Akbar's new religion is that it grew out of Sufi Islamic teachings, and he was able to cloak any heretical thoughts by still appearing as a Muslim ruler should even if it scandalized some of the clerics and aristocrats. However, formal conversion to Sikhism is outright apostasy. It will be very hard to retain complete loyalty of all the people he needs to maintain the Empire. Akbar already had to deal with some rebellions as a result of charges of heresy. As an actual apostate, he'll face a lot more challenges. It'll be war. Akbar will just have some loyal courtiers, Hindus, Sikhs, and other non-Muslims against established Muslim warriors. The most likely result is that he falls and a new dynasty is put in place. If Akbar secretly converts to Sikhism and starts a process of slowly preparing for the inevitable rebellion, then he might survive either as a much reduced empire, or in control of a complete empire. Even if he survives though, he and his empire will be greatly weakened.