Restart Course Trigger - Completion Status

I don't believe so, because the LMS status reflects whatever the "final" learner status is reported to it from the course. So restarting the course simply resets the course variables, etc. and allows the learner to "do it all over again as if it's the first time."

Your specific LMS may have some configuration that does in fact capture the completion status separate from a restart status, but since you have not noted which LMS you are using...

Good luck!