No. Her giving birth to Jesus wouldn't mean that He was her Savior too. Savior means deliverer. Preserver.
If Mary were without sin, then she would need no Savior.
If pain in childbirth were a punishment for original sin and Mary had no sin, original or otherwise, she also would not have died - since death was a punishment for sin as well.
Romans 5:12
Wherefore, as by one man sin entered into the world, and death by sin; and so death passed upon all men, for that all have sinned
Jesus was sinless, but He became Sin for us. He took our punishment which is why He died.
Mary died because she had committed sins in her life. She was a wonderful virtuous woman, but she was not sinless.
She was saved preemptively.
In order to be pure enough to carry and birth Jesus, Mary had to be born without original sin. Thus, Jesus was also the saviour of Mary.