It's going back a few decades, but I observed first-hand (several instances of) what happens when a 17-going-on-18 year old, who has been "supervised" consistently through the teen years, goes away to college. One of my first roommates from college arrived as a straight-laced farm-boy, and dropped out before his first semester was over after one OD and having gotten at least one co-ed pregnant. (The co-ed was also a nice girl from a nice family who's parents insisted that she never would have done "something like that" if it wasn't for the boy forcing her. Not even close to the truth, of course.) The other of my first roommates, who arrived at university just-about as conservative as the first, lasted a bit longer; mid-way through second semester. He didn't get a girl pregnant, but be sure that drugs and sex contributed to an academic predicament where his continuing at the university made little sense. My third roommate (I moved out of the wild drugs and sex dorm in the middle of the first semester) made it to Junior year, but I really don't know how, given how inadequately he was prepared to deal with being responsible for himself.
In my Junior and Senior years, I ran the hot-line, and I cannot count the number of freshman who were simply overwhelmed by the shock of their first, legitimate on-their-own experience. Their parents clearly did absolutely nothing to prepare them for practicing personal responsibility. They had the book-knowledge, of course - their parents and/or ministers outlined their behavioral expectations pretty-well, for sure - but these freshman had never experienced any short periods of personal recognizance. They went from being in the cradle of their parents' discretion to weeks-upon-weeks of being "unsupervised". It was a disaster for many.
Remarkably, this doesn't necessarily lead to a "Yes" answer to the poll question. A parent is absolutely responsible for the conduct of their minor children if they allow them to be unsupervised. If you don't feel that your teen is trustworthy enough to put your neck on the line like that - to do the "right thing" for a few days, at least - then you shouldn't allow this kind of thing.