No, one does not receive the Holy Spirit before being saved5. More specifically, the indwelling of the Holy Spirit is not given by God before one is baptized with water2,3,5,6 for the remission of their sins. This “rule” can be formulated by adding these facts together: (1) God gives the Spirit to all that obey Him1,6, and (2) Peter said anyone would receive the gift/promise of the Holy Spirit if they repent (obey1) and be baptized in the name of the Lord Jesus2,5,6. What Paul faced in Ephesus shows this rule play out5. These “disciples” (e.g. obedient believers) knew nothing of the Holy Spirit since they had only been baptized “into John’s baptism”5.
But wait! What about Cornelius3? This question serves to highlight the difference between two acts of the Holy Spirit often confused – the baptism of the Holy Spirit and the indwelling of the Holy Spirit. Technically, one could rightly argue that the Gentiles in Acts 10 “received the Holy Spirit”3 before being saved. However, Cornelius shows us that the baptism of the Holy Spirit was not for the benefit of Cornelius! It wasn’t for his salvation, but to convince Peter that Gentiles were equal to Jews4, worthy to receive the indwelling of the Holy Spirit through their belief/obedience1. Furthermore, Peter would later equate Cornelius’ baptism of the Holy Spirit to what had happened only once before “at the beginning” on the day of Pentecost4.