Yes, demerit points are assigned for all moving violations in Virginia.  The Virginia Department of Motor Vehicles classifies moving violations as either three point violations, four point violations or six point violations.  According to the Virginia DMV, most Reckless Driving offenses are six point violations, although one type of Reckless Driving in Virginia is only a four point violation

According to the Virginia DMV, demerit points remain on your record for two years from the date the offense was committed

People often confuse the date on which demerit points are removed from a Virginia DMV record with the date on which the convictions are removed from a Virginia DMV record (depends on the severity of the offense.  Demerit points will be removed from the Virginia DMV record 2 years from the date of the offense, but the length of time convictions will remain on the record depends on the severity of the offense - and some may be on the Virginia DMV record permanently.