Yes, Jehovah’s Witnesses believe that the New Covenant is open to Gentiles. However, they believe that only 144,000 persons since the time of Jesus can be sealed and anointed by Jehovah’s spirit, enter into the New Covenant and have Christ Jesus as their mediator. They believe that since 1919, when they were chosen as Jehovah’s earthly representatives, the “anointed remnant” of the 144,000 have replaced Israel as Jehovah’s chosen people. They see this small number of anointed Jehovah’s Witnesses as being “spiritual Israel.”
Insight on the Scriptures, Volume 1 Great Crowd: On the other hand, the view that here Christians of Jewish stock are being distinguished from Gentile Christians runs counter to the apostle Paul’s inspired statement that fleshly distinctions are of no consideration in the Christian congregation, its members being all one in union with Christ Jesus. (Ro 10:12; Ga 3:28)... It thus seems clear that the 144,000 sealed ones are of spiritual Israel, not fleshly Israel—hence include both Jewish and Gentile Christians.—Galatians 6:16. Source: https://wol.jw.org/en/wol/d/r1/lp-e/1200001762
Prior to 1919 they acknowledge that the first Christians (mainly Jews) were members of the New Covenant, who belonged to the 144,000 who will rule, in heaven, alongside Christ Jesus. After the first century, apostasy set in and it wasn’t until the start of the 20th century that “true worship” was restored. That means most of the “anointed remnant” of the 144,000 who are in the New Covenant must now be Gentile Jehovah’s Witnesses. They alone can partake of the bread at wine at the annual memorial of Christ’s death. That’s because they alone have a heavenly hope and they alone are in the New Covenant. The other Jehovah’s Witnesses (8 million or so) are not in the New Covenant, they do not have Christ Jesus as their mediator, and they do not have a heavenly hope. They come under the category of “the other sheep”:
Watchtower 1998 2/1 pp. 18-23 The Other Sheep and the New Covenant: 3 For the 144,000, the blessing of the Abrahamic covenant is administered through the new covenant. As participants in this covenant, they come “under undeserved kindness” and “under law toward Christ.” (Romans 6:15; 1 Corinthians 9:21) Hence, only the 144,000 members of the Israel of God have properly partaken of the emblems during the Memorial of Jesus’ death, and only with them did Jesus make his covenant for a Kingdom. (Luke 22:19, 20, 29) Members of the great crowd are not participants in the new covenant. However, they associate with the Israel of God and live with them in their “land.” (Isaiah 66:8) So it is reasonable to say that they too come under Jehovah’s undeserved kindness and under the law toward Christ. While not participants in the new covenant, they are beneficiaries of it. Source: https://wol.jw.org/en/wol/d/r1/lp-e/1998085?q=beneficiaries+new+covenant&p=par
Watchtower 2010 3/15 pp. 24-28 One Flock, One Shepherd: 13 Jesus referred to this new covenant on the night before his death when he said: “This cup means the new covenant by virtue of my blood, which is to be poured out in your behalf.” (Luke 22:20; 1 Cor. 11:25) Are all Christians included in this new covenant? No. Some, like the apostles who drank of that cup that evening, are participants in the new covenant.* Jesus made another covenant with them to rule together with him in his Kingdom. (Luke 22:28-30) They will share with Jesus in his Kingdom.—Luke 22:15, 16. Source: https://wol.jw.org/en/wol/d/r1/lp-e/2010202?q=beneficiaries+new+covenant&p=par
Jehovah’s Witnesses believe that the New Covenant is still in force today for Jews and for Gentiles who are part of ‘spiritual Israel’, not ‘fleshly Israel’. However, they say the new covenant is now only open to Jehovah’s Witnesses who are part of the “anointed remnant” of the 144,000.