Does the Sai Satcharita mention any instances where Udi helped people who had trouble sleeping?

Yes, Chapter 33 of the Shri Sai Satcharita provides two specific examples of Udi curing sleep-related problems in a footnote by R. Hari Sitaram Dixit. In the first case, a friend of Dixit's had been unable to sleep for eight days and found no relief from a doctor's medicine. After Dixit gave him Baba's Udi to take for three days, the friend reported the very next day that he had slept soundly through the night after taking the Udi just once. Similarly, another friend's child from Bandra had not been able to sleep for two months. When the father took the child to Shirdi for Baba's Darshan, the child got sleep that very night and continued to sleep well thereafter.