If he ended up in genpop, he would still get beat up, even in a minimum security prison, I think. Many people would not want to add more to their prison time, but with somebody as high profile as Chris combined with the nature of his crime, an inmate might consider it their "duty" to beat the crap out of Chris. After all, Jared Fogel is in a minimum security prison, and he still got attacked by a 60 year-old inmate for being a sex offender.
Either way you look at it, Chris would probably have a huge metaphorical target on his head if you tried putting him in with the rest of the prison population no matter what level of security the facility is.