The Scriptures go into a lot of detail when it comes to describing the death of Jesus on the cross. They make it very clear that He was dead before the other two that were crucified with Him and before He was put in the tomb.

And bowing His head, He gave up His spirit.
31 Therefore, because it was the Preparation Day, that the bodies should not remain on the cross on the Sabbath (for that Sabbath was a high day), the Jews asked Pilate that their legs might be broken, and that they might be taken away. 32 Then the soldiers came and broke the legs of the first and of the other who was crucified with Him. 33 But when they came to Jesus and saw that He was already dead, they did not break His legs. 34 But one of the soldiers pierced His side with a spear, and immediately blood and water came out. 35 And he who has seen has testified, and his testimony is true; and he knows that he is telling the truth, so that you may believe. 36 For these things were done that the Scripture should be fulfilled, “Not one of His bones shall be broken.” 37 And again another Scripture says, “They shall look on Him whom they pierced.

It would have been more than their lives were worth for the soldiers not to have ensured Jesus was dead before deciding not to break His legs. They were experienced and had seen dead bodies many times so they knew what they were looking at. Nevertheless, in an excess of caution, they pierced His side and punctured His heart. Doctors tell us that another sign He was dead (i.e. well and truly dead) was that the blood residing in heart had separated into blood and water because it hadn’t moved in some time. His heart hadn’t been beating for a while before the soldier pierced it.

Later, in Romans, Paul makes the surprising statement that the only way we can deal with sin is to understand that when Jesus died our sin nature died with Him (Romans 6:3-7). By believing this we receive that grace and can rest in that finished work.

So, the fact that Jesus died is very important.