Can one receive the Holy Spirit without baptism?
The clear answer to this is "yes." Baptism is a command found in the New Testament, yet people had received the Holy Spirit in the Old Testament. In addition:
"While Peter was still speaking these words, the Holy Spirit fell upon all those who heard the word. And those of the circumcision who believed were astonished, as many as came with Peter, because the gift of the Holy Spirit had been poured out on the Gentiles also. For they heard them speak with tongues and magnify God. Then Peter answered, "Can anyone forbid water, that these should not be baptized who have received the Holy Spirit just as we have?" And he commanded them to be baptized in the name of the Lord. Then they asked him to stay a few days" (Acts 10:44-48).
Cornelius and his household received the Holy Spirit prior to baptism. In fact, it was because God showed His acceptance of the Gentiles by giving them gifts of the Holy Spirit that the Jews were finally convinced that the Gentiles could be saved like they and baptism was offered. See: When Was Cornelius Saved?
What you did not ask is whether receiving the Holy Spirit proved that a person was saved. The answer here is "no." See "Is the Spirit only given to the obedient?" for detailed proof. If receiving the Holy Spirit indicated salvation, then there would no need for Cornelius' household to be baptized since baptism is for the forgiveness of sins (Acts 2:38), to wash away sins (Acts 22:16), and to save (Mark 16:16; I Peter 3:21). Yet even after receiving the Holy Spirit, Peter commanded that Cornelius and his household be baptized. Therefore, Peter speaking by the inspiration of the Spirit proves that God did not yet concern these people saved from their sins.