Does the Sai Satcharita mention any instances where Udi helped people who were suffering from sleeplessness?

Yes, Chapter 33 includes a footnote by R. Hari Sitaram Dixit that provides two specific examples of Udi curing sleeplessness. In the first case, a friend of Dixit came to him after suffering from insomnia for eight days, finding no relief from a doctor's medicine. Dixit gave him Maharaj's Udi to take for three days, and the very next day, the friend reported that he had slept soundly through the night after taking the Udi. In a similar account, a friend's child from Bandra had not been able to sleep for two months. After the father took the child to Shirdi for Maharaj's Darshan, the child slept soundly that very night and continued to do so from then on.