In OBS you can do stream, file, or stream+file.
I record all of my games to the hard drive whether I stream them or not, then save or delete them depending on whether anything interesting happens. Keeping the file output turned on is a good idea because the broadcast copy is always "choppier" than the local copy, which probably has to do with either the connection or how Twitch processes the video, I don't know.
The only problem is that if the stream goes down, like if your Internet connection dies, you'll get an error and the recording will stop. I hate that. It should just alert you that the connection has been lost, but continue to record to the file. Maybe I'll suggest that to them.