The logs are there to catalog occurrences and send them to Apple for review. They do not represent crashes, those are filed under specific crash reports (SIGSEV, SIGABUS, etc.). The awdd logs are tied to the awd daemon (awdd) and have nothing to do with battery performance and everything to do with data collection. Disabling "automatically send diagnostic and usage data" to Apple stops the awdd process from running and the subsequent logs from being generated. The logs typically record anomalies in iOS, not explicit crashes. These anomalies generally can lead to systemic problems (like iTunes failing to find your device during a wireless sync) that fall outside of a specific service crash.
I believe the logs are permanently stored to help Apple technicians should they ever service the phone. I have been unable to clear them out (a sync with iTunes transfers the crash logs to your Mac).
In any case, the files are tiny (byte sized), and help Apple collect data to better tailor their software. They are also anonimized so you shouldn't worry about privacy. Leave the awdd process active or not entirely depends on you, but don't worry about the logs. They have no relevance to battery performance.