We want to use google-cloud-speech to perform streaming speech-to-text conversion. If we enable data logging, will the audio data and the recognition metadata be saved in bucket associated with project?
No, and in fact, it's typically the other way around. You can upload your audio file to a Cloud Storage bucket, and the Speech API can read directly from that using a gs:// URL that you provide.
According to the documentation, Data logging just is for allowing Google to improve its models using the data you provide. It's not for remembering everything you ever did with the API.