I wouldn't think they would. They want to isolate him and break his spirit, to make plea bargaining easier, or possible. His appeal to the public was transcribed from a phone call to his legal team which posted it to the world on a website dedicated to Mangione's defense.

"#LuigiMangione has violated special treatment (🤔) and shouldn't get to use a laptop, Manhattan prosecutors say"
https://www.cbsnews.com/newyork/news/luigi-mangione-unitedhealthcare-ceo-killing #DeadCEOGoodCEO