Easy reply to the title query: No.
The variety of workers within the non-public sector really fell by 2.166 million. So why did the BLS report an enormous improve in jobs? Seasonal adjustment.
Alan Reynolds makes this level in “Can a Seasonal Adjustment to Misplaced Jobs Justify a Tighter Fed?,” Cato at Liberty, February 6, 2023.
The variety of jobs just about at all times falls between December and January as varied retailers and producers lay folks off whom they employed for the Thanksgiving to Christmas season.
Seasonal adjustment is useful and essential. However you need to bear in mind whether or not you’re citing seasonally adjusted information or precise information.