In order to answer the question we must first look at what might be meant by the term "spiritual body." If the term means that the spiritual body was not physical, then the answer is no; His body was not changed.
Jesus was physically raised from the dead (John 2:19-21; Luke 24: 39; 1 Cor. 15:1-4). He retained the crucifixion wounds after His resurrection (John 20:27) and is still called a man (1 Tim. 2:5). Also, Acts 1:11 says, “and they also said, 'Men of Galilee, why do you stand looking into the sky? This Jesus, who has been taken up from you into heaven, will come in just the same way as you have watched Him go into heaven.'”
So we can see that Jesus rose physically, retained the crucifixion wounds, is still called a man, and will return the same way He was seen ascending to Heaven--which was physically ascending in His physical body. Therefore, Jesus' resurrected body did not change into a non-physical body at His ascension.