Yes - Reaper "streams" the audio data onto the storage device.
I started using Reaper for this reason alone, because my field recorder might lose power mid-session.
You can set how often Reaper closes the streamed files in the recording setups. Even with a streaming system, the last files open will not be closed properly if power fails, so having Reaper save every 5 minutes or so (based on file size) will mean that only the last 5 minutes of files will not be closed properly. I believe Reaper can recover these files as well, but I forget how (never had to do it).
Mahope Kakou (Later Dudes)...