I've heard Udi can help with sleep issues. Are there any examples of this in the Sai Satcharita?

Yes, Chapter 33 provides two distinct examples of Udi curing sleeplessness, as noted by R. Hari Sitaram Dixit. In the first case, a friend of Dixit's came to his office complaining of being unable to sleep for eight days, despite taking a doctor's medicine. Dixit gave him some of 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. Similarly, a friend's child from Bandra had not been able to sleep for two months. The father took the child to Shirdi for Baba's Darshan, and that very night, the child got sleep and continued to sleep well every night thereafter.