Most likely, yes, and many people have said that there is no way to kill yourself in these facilities. Between the floor and the ceiling is little room for space, and there is no way for someone to link to anything.
The sheets in Epstein's cell were not strong enough compared to his weight. There is also no way to commit suicide from the bed because there is a solid steel frame. There is no light fixture and no bars. Also, many of the guards in these places are on a power trip, so they are happy to see a prisoner have a nervous breakdown, and they often assist in breaking them.