Fat chance. In Matthew, Mary doesn't leave the tomb until she is made perfectly well aware of what happened to the body of Jesus:
NAU Matthew 28:1 Now after the Sabbath, as it began to dawn toward the first day of the week, Mary Magdalene and the other Mary came to look at the grave.
2 And behold, a severe earthquake had occurred, for an angel of the Lord descended from heaven and came and rolled away the stone and sat upon it.
3 And his appearance was like lightning, and his clothing as white as snow.
4 The guards shook for fear of him and became like dead men.
5 The angel said to the women, "Do not be afraid; for I know that you are looking for Jesus who has been crucified.
6 "He is not here, for He has risen, just as He said. Come, see the place where He was lying.
7 "Go quickly and tell His disciples that He has risen from the dead; and behold, He is going ahead of you into Galilee, there you will see Him; behold, I have told you."
8 And they left the tomb quickly with fear and great joy and ran to report it to His disciples. (Matt. 28:1-8 NAU)
But in John, Mary is at the tomb, then she runs and complains to Peter and John that she doesn't know what happened to Jesus' body:
NAU John 20:1 Now on the first day of the week Mary Magdalene came early to the tomb, while it was still dark, and saw the stone already taken away from the tomb.Apologists dismiss this by speculating either a) Mary in Matthew split off from the group of other women before they got to the tomb, wasn't there to recieve the angelic report, and John is talking about Mary after she comes back from the detour having missed the show, or b) Mary was told what happened to Jesus' body along with the other women, but because of what's written in John, apparently the truth just hadn't "hit" her just yet (!?)
2 So she ran and came to Simon Peter and to the other disciple whom Jesus loved, and said to them, "They have taken away the Lord out of the tomb, and we do not know where they have laid Him." (Jn. 20:1-2 NAU)
Here's how you stomp the guts out of these speculations and force inerrancy to reveal its ugly head:
All patristic sources and most modern Christian scholars agree that John was written later than the other 3 canonical gospels.
If then you read Matthew's account the way it was originally intended (i.e., by itself, without comparing it to other accounts), you discern not the slightest justification for supposing Mary split off from the group of women before they got to the tomb.
Concerning Gleason Archer's "the truth just hadn't hit her just yet" to explain her ignorance in John, again, if you read Matthew 28:7-8 as it was orignally intended to be read (without worrying about comparing it to or reconciling it with some other account), the statement in v. 8 would be taken by you to mean that Mary, after learning what happened to the body, left with the other women and told the men the same thing the angel said.
If you read Matthew objectively as it was originally intended by its author, you get not the slightest justification to think Mary either departed from the group before they hear the angel, nor that she experienced a failure of comprehension between the angelic announcement and her reporting to the other disciples.