Question: Can a recruit go on an official visit during quite period?
Answer: Quiet Period Visits Quiet periods only apply to Div. I colleges. During this time, the coaches may continue normal recruiting, but they are not allowed to scout off campus. Official---and unofficial---visits are definitely permitted as long as you've started your junior year in high school.
Note: The primary/longest quiet period for softball runs from Thanksgiving to New Years. That's why you won't see D-I coaches at travel tournaments held between those dates.