Probably yes, depending on the complexity of the system. You are permitted to update software in an avionic system, provided that the following three conditions are met. (Reference: Part 66 MOS, Page 6)
- The system has a discrete test function to confirm success of the updating
- The serviceability of any other system affected by the system is also confirmed
- Only simple tests (i.e. “Push a test button with a Yes/No result”) are required to verify serviceability