To commence with a one–word answer would gender confusion because of the way that the question is formulated. The question involves three things: baptism, the breaking of bread and fellowship. The first is linked to the Kingdom, the other two to the Assembly.
Baptism is the outward public expression of being in the kingdom, whether real or unreal. Similarly, breaking bread (partaking of the Lord’s Supper) is the outward public expression of being in the Assembly, whether real or not. Now the moment a person is converted he is a subject of the kingdom, and a member of the body of Christ, the Assembly, even if he does not realise it himself. Such an individual may indeed have been converted in isolation simply by reading the Scriptures. However, being in isolation, he cannot give public expression to his faith, either by being baptised or breaking bread––he needs someone to baptise him, and other Christians to break bread with.
Baptism is the outward expression of an individual’s submission (at least nominally) to the authority of the Lord. Having submitted to baptism, a person has owned the Lord’s authority and “put on Christ” (Gal. 3: 27). The kingdom is thus the sphere of profession.
Similarly, partaking of the Lord’s Supper is the outward expression of the fellowship of the body of Christ. Fellowship is essentially what those who have believed the Gospel have in common. The Bible acknowledges but one fellowship: “[the] fellowship of his Son Jesus Christ our Lord” (1 Cor. 1: 9). Yet to work out the truth of the one body of Christ practically (see 1 Cor. 12: 12–27) fellowship must involve others––such matters cannot be worked out in isolation.
Fellowship and the breaking of bread are identified with the Assembly; baptism is identified with the Kingdom as the domain of profession. Now profession is a wider sphere than the Assembly. These two concentric circles may be seen in Eph. 4: 4-6. “[There is] one body and one Spirit, as ye have been also called in one hope of your calling” is the inner circle, the Assembly. Embracing the Assembly, is an outer circle: “one Lord, one faith, one baptism” which is the Kingdom. All who outwardly, in profession, own the authority of the “one Lord” and confess to the “one faith” (what they profess to believe, whether real or otherwise) are in the Kingdom and are there by the “one baptism”. The Kingdom is the sphere of profession, whether real or not, and baptism is the means of entrance. Hence baptism is identified with the Kingdom, not the Assembly.
In NT days, the question of baptism preceding the breaking of bread would never have been raised for baptism was always immediate. For example, when Philip preached “the glad tidings of Jesus” (Acts 8: 35) to the Ethiopian eunuch, his preaching must have involved the necessity of baptism and its immediacy for it is the eunuch who says “Behold water; what hinders my being baptised?” (v36). The matter could not wait. Take the more powerful example of the Philippian jailer. Paul and Silas “spoke to him the word of the Lord, with all that were in his house” (Acts 16: 32). That “word of the Lord” must again have involved the truth of baptism since the baptism of the household could not even be delayed until the morning––though it was after midnight when he was converted (vs 25-33). The modern idea in the western world of a meeting for a baptism being arranged days, weeks and even months ahead is foreign to the Scriptures.
Hence the normal series of events as presented in the Bible would be as follows. A person is converted and, as a consequence, immediately becomes a member of the body of Christ. Straight away he is baptised, and subsequently breaks bread with other Christians. Now a person breaking bread who has never been baptised is in an anomalous position: he is publicly identifying himself with the Assembly by breaking bread but has not publicly owned the Lord’s authority in baptism. Of course, as already stated, baptism has no direct link to the Assembly, and to insist on a person being baptised before he is allowed to break bread is to forge a link that is absent in Scripture. However, should a person have the truth of baptism brought before him and he refuses to submit to it, then that would be serious indeed. In those circumstances it would call into question the reality of his profession and prohibit him from breaking bread.
