Those are only two of the things done by the Holy Spirit. But there is no question whatsoever that Spirit baptizes or joins each believer to the Body of Christ. For by one Spirit are we all baptized into one Body, whether we be Jews or Gentiles, whether we be bond or free; and have been all made to drink into one Spirit. (1 Cor 12:13).
καὶ γὰρ ἐν ἑνὶ πνεύματι ἡμεῖς πάντες εἰς ἓν σῶμα ἐβαπτίσθημεν εἴτε Ἰουδαῖοι εἴτε Ἕλληνες εἴτε δοῦλοι εἴτε ἐλεύθεροι καὶ πάντες εἰς ἓν πνεῦμα ἐποτίσθημεν
Agreed - the Holy Spirits ministry is vast in its operation and if one is in the "Body of Christ" then that one was placed or immersed into that Body by the Spirit. I like what John Gill had to say on this verse:
For by one Spirit are we all baptized,.... This is to be understood not of water baptism; for the apostle says not in one, and the same water, but "by", or "in" one Spirit, are we all baptized; the baptism of water, and of the Spirit, are two different things; see Mat_3:11. Besides, all that are baptized in water, are not baptized in or by the Spirit, as the case of Simon Magus, and that of others, show; nor does water baptism incorporate persons into the church of Christ; neither into the invisible church, which is the body of Christ, and here meant; nor into a visible Gospel church state; they being indeed true believers, and baptized, are proper persons to be received into a church; but baptism itself does not put them into it, or make them members of it: persons may be baptized in water, and yet may never be joined to a church. There is indeed an allusion made to water baptism, but it is the grace of the Spirit in regeneration and sanctification which is here intended; which grace, both in the Old and in the New Testament, is frequently signified by water, and called a baptism, or a being baptized, because of the plenty, abundance, and superabundance of it, then bestowed; and is expressed by floods and rivers, and a well of living water; and is what qualifies and fits persons for the ordinance of water baptism. Now this is wrought by the Spirit of God, and is owing to his divine power and energy; not to water baptism, which has no regenerating virtue in it; nor to carnal regeneration, or a being born of blood, or of the best of men; nor to the will of any man; nor to the will of the flesh, or the power of man's freewill; but to God, to the Spirit, who is Lord and God, and the only sanctifier of the sons of men; by which spiritual baptism, or by whose grace in regeneration and conversion they are brought into one body: the mystical body of Christ, the universal and invisible church; that is, openly and manifestatively; for otherwise it is the grace of God in election, and in the everlasting covenant, choosing them in Christ, as members in their head, and constituting them such, that puts them among that number; but spiritual baptism, or the sanctifying grace of the Spirit, makes them appear to belong to that body, and makes them meet for, and gives them a right unto, a particular Gospel church, and the privileges of it, which the Spirit of God directs and brings them to. Whether we be Jews or Gentiles, whether we be bond or free; it matters not of what nation, or of what state and condition of life persons be; if they are regenerated and sanctified, they appear equally to belong to Christ, to be of his body, and have an equal propriety in all immunities and blessings belonging to his people; see Col_3:11
and have been all made to drink into one Spirit; are all partakers of the same graces of the Spirit, as faith, hope, love, &c. and daily receive under his guidance, direction, and influence, out of the same fulness of grace in Christ, from whence they draw and drink this water with joy; and all drink the same spiritual drink, the blood of Christ, whose blood is drink indeed: and there may be in this clause an allusion to the ordinance of the supper, as in the former to the ordinance of baptism. Moreover, all new born babes, as they desire the sincere milk of the word, so they drink of it, and are refreshed with it, and are nourished by the words of faith, and sound doctrine, under the application, of the Spirit; and being trees of righteousness, and the planting of the Lord, the Spirit, they are watered by his grace, under the ministrations of the Gospel; and as they become one body under Christ, the head, so they are made to drink into one Spirit, or to become of one heart and soul with one another, being knit together in love, the bond of perfectness.