Running smoothieware, no. The only controllers that log actual laser on time are DSP controllers like the Ruida.
We did recently add a job log in v0.9.10 that you can enable by going to Edit > Settings > File Settings and click the “Save Job Log” check.
All this does though is log which project file was run, on which profile, and at what time. But not actual laser on time.
For gcode controllers it would probably be possible to at least update this to log how long each stream was running but that’s about it. It would be very difficult to break that down into actual laser on time vs just rapid moves. But honestly for most jobs that time wouldn’t be all that different.
I will discuss it with the rest of the team.