You can get the headers from Update
object, add your own and put them back before executing the HTTP request:
final Update update = mService.files().update(mDriveFile.getId(), mDriveFile, byteContent);
final HttpHeaders headers = update.getRequestHeaders();
headers.setIfMatch("TheETagStoredFromDownload");
update.setRequestHeaders(headers);
mDriveFile = update.execute();