Using Solspace Craft Calendar plugin, how can I get random events within a defined timeframe?
UPDATE: This issue has been fixed as of Calendar 1.8.4 on April 21, 2017.
https://solspace.com/craft/calendar

Your above code should work. I think there might be a bug with the loadOccurrences: false parameter used in conjunction with the limit: 3 parameter. Try increasing the limit to something higher and see if you get results. :)

In the meantime, I've logged this bug and we'll have a bug fix for this in the near future. Sorry for the inconvenience.