False. One member of our family of seven tested positive at the airport upon arrival (after testing negative before departure). Received some phone calls and emails from the Misrad Habriut, but we ignored them and they stopped after around 2 days. Had no issue leaving two weeks later.
Two weeks later is never an issue since it's beyond the quarantine requirements.
However I know several people who couldn't leave within 3-4 days, including one who had his passport confiscated for voluntarily breaching quarantine.