Local does a pretty good job of scrubbing private info from the logs and the errors it produces, however there’s always the possibility that something private can come through. Because these are public forums, always review the screenshots you are sharing to make sure there isn’t private info like passwords being displayed.
I think it can partially work but Local will still need space on the machine to be able to operate. See this comment from Ben for example:
If you have a lot of projects in Local you could also backup and export them to move to your external hard drive for storage and simply remove them from Local when you are done. If you ever need to revisit you could import the zip file back into Local.