Does the Satcharita suggest that Sai Baba is still present and active after his Mahasamadhi? If so, where and how?

Yes, Chapter 43 strongly affirms Sai Baba's continued presence. It states that he did not perish but merged into the unmanifest, remaining 'firmly imprinted in the hearts of devotees.' Even in this unmanifest state, he enjoys his true self and 'always keeps the devotees awake.' The text explicitly says that this 'beginningless and endless Sai will remain unbroken even at the end of the universe.' Furthermore, it claims his influence is still proven today, as devotees receive experiences according to the feeling in their minds. He is described as filling the entire 'moving and non-moving world' in his true form as a powerful, miraculous avatar.