Correct, record mode is independent of editing. The main difference between the two recording modes is that Comp mode is intended to leave only one take active after recording stops, automatically muting the overlapped parts of previous takes, while Sound on Sound is intended for layering parts that will all remain audible.
When loop-recording, previous takes will be inaudible
while recording regardless of the mode (much to the chagrin of users who want to layer loops in real time performance with Sound on Sound), but you'll have to manually mute the takes you don't want to hear on playback. If you restart the transport between takes, you'll hear previous takes in Sound on Sound mode, but they'll be muted in Comp mode.