Here we go. The Sox 1st round pick will be protected. The following is from last year, but the Sox will fall in the same category this winter as well. They lose a 2nd if they sign a player who had a QO extended to them. If they sign 2 players that had QO's extended to them, it's a 2nd and a 3rd that they lose. Either way they keep their first round pick.
https://www.mlb.com/news/draft-picks-for-2018-19-qualifying-offers-c300535882
Penalties for signing players who reject QOs
Any team that signs a player who has rejected a qualifying offer is subject to the loss of one or more Draft picks. However, a team's highest first-round pick is exempt from forfeiture, which is a big change that went into effect with the new CBA. Three tiers of Draft-pick forfeiture -- based on the financial status of the signing team -- are in place to serve as a penalty for signing a player who rejected a qualifying offer:
• A team that exceeded the luxury tax in the preceding season will lose its second- and fifth-highest selections in the following year's Draft, as well as $1 million from its international bonus pool for the upcoming signing period. If such a team signs multiple qualifying-offer free agents, it will forfeit its third- and sixth-highest remaining picks as well.
Teams that are in this group this offseason: Nationals, Red Sox
• A team that receives revenue-sharing money will lose its third-highest selection in the following year's Draft. If it signs two such players, it will also forfeit its fourth-highest remaining pick.
Teams in this group: A's, Braves, Brewers, D-backs, Indians, Mariners, Marlins, Orioles, Padres, Pirates, Rays, Reds, Rockies, Royals, Tigers and Twins.
• A team that neither exceeded the luxury-tax threshold in the preceding season nor receives revenue sharing will lose its second-highest selection in the following year's Draft, as well as $500,000 from its international bonus pool for the upcoming signing period. If it signs two such players, it will also forfeit its third-highest remaining pick and an additional $500,000.
Teams in this group: Angels, Astros, Blue Jays, Cardinals, Cubs, Dodgers, Giants, Mets, Phillies, Rangers, White Sox and Yankees.