Yes, Jesus is like us in all things except sin (iirc, that’s from the Epistle of St. Paul to the Hebrews).
However, Our Lord Jesus Christ, the Son of God, is the Second Person of the Holy Trinity with two natures, Divine and human, in the unity of His Divine Person. And according to St. Paul, He is the New Adam (c.f. Romans).
When the first Adam was created, he had a perfect human nature not subject to illness, concupiscence, death or decay.
The same applies to Eve. She had the same prerogatives as Adam. It wasn’t until Adam & Eve sinned that they were stripped of the preternatural gifts of immortality, integrity etc (sorry, I forget the other two). Then they were subject to ignorance, illness, old age and death.
Had Adam & Eve not sinned, things would be very different today (e.g. we’d all be immortal).
Since Jesus IS the New Adam and Mary is the New Eve, then they must be superior to the old Adam & Eve. Therefore, they must have all the prerogatives of the old Adam & Eve and even more, like St. Irenaeus says: “Death through Eve, life through Mary.”
Therefore, they would have not been subject to bodily death since death is one of the effects of original sin. As I previously posted, Jesus willingly died on the cross for our salvation. Mary fell asleep out of pure love for God.
Does that help?