The short answer is No.
The Web Speech Api Specification does not prohibit this (the browser could allow the end-user to choose a file to use as input), but the audio input stream is never provided to the calling javascript code (in the current draft version), so you don’t have any way to read or change the audio that is input to the speech recognition service.
This specification was designed so that the javascript code will only have access to the result text coming from the speech recognition service.