I picture it being on a similar level of horrifying as a hypothetical incarceration picture taken of Michael Jackson, had he actually been sentenced to prison in the early 2000s.
He was deeply insecure about his appearance, and spent a lot of time and money daily on hair/wig/skin treatments, makeup, even special lighting for interviews. Being in prison without access to those things, you can bet that a year (hell, a month) in, he would’ve looked like a Chernobyl radiation victim.
I expect JY’s mugshot to be pretty fucking appalling, but since he doesn’t put any effort into his appearance as is, I’m probably being optimistic.