No. First of all, 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 (napha) 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" (v. 5). 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. The apostle Paul couldn't heal Timothy's stomach problem (1 Timothy 5:23) nor could he heal Trophimus at Miletus (2 Timothy 4:20) or Epaphroditus (Philippians 3:25-27). Paul spoke of "a bodily illness" he had (Galatians 4:13-15). He also suffered a "thorn in the flesh" which God allowed him to retain (2 Corinthians 12:7-9). God certainly allowed Job to go through a time of physical suffering (Job 1--2). In none of these cases is it stated that the sickness was caused by sin or unbelief. Nor did Paul or any of the others act as if they thought their healing was guaranteed in the atonement. They accepted their situations and trusted in God's grace for sustenance. It is noteworthy that on one occasion Jesus indicated that sickness could be for the glory of God (John 11:4).
Finally, there are numerous verses in Scripture which reveal that our physical bodies are continuously running down and suffering various ailments. Our present bodies are said to be perishable and weak (1 Corinthians 15:42-44). Paul said "our outer man is decaying" (2 Corinthians 4:16). Death and disease will be a part of the human condition until that time when we receive resurrection bodies that are immune to such frailties (1 Corinthians 15:51-55).
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.
