SpeechRecognizer is a way of connecting apps to speech recognizers. These speech recognizers extend RecognitionService. Some of these speech recognizers might do offline recognition, some of them might claim that they do, but actually don't. So if you have privacy concerns then rather implement your own recognizer.
The other question is if speech recognition is the right tool for voice activity detection.
Regarding the API to the speech recognizer, i.e. the constants in RecognizerIntent, there is no boolean for online/offline or anything specific for voice activity.