For possession of child pornography, house arrest is not a realistic outcome regardless of health status or lack of prior criminal history. Federal law and most state statutes treat child pornography offenses as serious felonies with mandatory minimum sentences that require incarceration. A clean record and genuine remorse factor into sentencing to some degree, but they do not move the needle far enough to result in house arrest on these charges. Judges have very limited discretion to deviate from the sentencing framework that applies.
Serious illness is a separate but related issue, and it does matter, just not in the way most families hope.
If someone is genuinely medically compromised, with conditions as significant as cancer, serious heart disease, and COPD, the Bureau of Prisons and state corrections departments have mechanisms to address that. The most relevant is designation to a federal medical center or a prison facility with a hospital unit equipped to handle complex medical needs. FMC Devens, FMC Butner, FMC Rochester, and a handful of others exist specifically to house inmates who require ongoing medical care that a standard facility cannot provide.
There is also Compassionate Release, formally called a Reduction in Sentence, which can be pursued if the medical situation reaches a terminal or severely debilitating level. That process involves a formal petition and is granted at the discretion of the warden and ultimately the court. It is not common, but it is a legitimate avenue when the medical circumstances are serious enough.
The family's energy is best directed toward ensuring he gets designated to a facility equipped for his medical needs, and consulting with an attorney about whether compassionate release is worth pursuing given the specifics of his condition.