I think Local 2.0.3 does a headless and background start to VirtualBox. This is why we no longer see it running. But Local’s log file documents starting and stopping it.
The main reason why there were issues with 2.0 (and then resolved in 2.0.3) was due to the addition of NFS for Docker Volumes. If NFS refused to connect, it had no fallback so the machine would never fully start up with docker-machine start. I’m guessing the headless start worked because it bypassed docker-machine's startup script.
2.0.3 added a fallback so if NFS fails to connect, it will go back to vboxsf. Then, we added a switch under Preferences » Advanced to manually toggle this.