No, while ultimate physical healing is in the atonement (a healing we will enjoy in our resurrection bodies), healing of our bodies while in the mortal state (prior to our death and resurrection) is not guaranteed in the atonement.
Moreover, it is important to note that the Hebrew word for healing (rapha) can refer not just to physical healing but to spiritual healing. The context of Isaiah 53:4 indicates that spiritual healing is in view. In verse 5 we are clearly told,
“He was pierced through for our transgressions,
He was crushed for our iniquities;
The chastening for our well-being fell upon Him,
And by His scourging we are healed.” —Isaiah 53:5 NASB
Because “transgressions” and “iniquities” set the context, spiritual healing from the misery of man's sin is in view.
Further, there are numerous verses in Scripture which substantiate the view that physical healing in mortal life is not guaranteed in the atonement and that it is not always God's will to heal.
Am I saying we shouldn't pray for healing? No, not at all. I'm just saying that after we've asked for healing, we need to submit to God's sovereign will. He may have a purpose in allowing our illness.
Author: Dr. Ron Rhodes of Reasoning from the Scriptures Ministries.
“Are We Physically Healed by Jesus' Stripes?
Isaiah 53:5” by Cameron Buettel, Grace to You (2016) (off-site)
Did God make the world the way it is now? What kind of world would you create? Answer
ORIGIN OF BAD THINGS—How did they come about? Answer
Fall of man and death’s beginning
What is SIN?
Why does God allow innocent people to suffer? Answer
What about the issue of suffering? Doesn't this prove that there is no God and that we are on our own? Answer
Does God feel our pain? Answer
Miracles of the Bible
The man named Job and the Book of Job
What about the Psalm 91 promises? (“…no harm will befall you, no disaster will come near your tent…”) Answer
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