No, it won't, instead it will run every 3 minutes (* == At any minute, /3 == every 3, */3 every 3 minutes, no matter what minute). AFAIK it's not possible to create a crontab entry for anything less than every minute.
If you really need to run something every 20 seconds, rather write a script that backgrounds and starts the desired action in a loop (using sleep or something alike).
Yes, that would run your script every minute. But I would still advise that any activity that has to run in such short intervals should rather be implemented as some kind of daemon (or daemon-like script), rather than be invoked by cron.