If the plural of anecdote is data, when the ACA was first rolled out, someone close to me discovered they had colon cancer. They had been having symptoms for quite some time, but had been managing them with home treatment, the first day the had insurance they went to get it checked out. Lucky they did, as devastating as it was (and continues to be, turns out your chemo is brutal and having large sections of your colon removed isn't great either) their doctors already weren't sure they could treat it effectively.
While they credit the ACA with saving their life, had we had some form of socialized medicine from the start, this likely would've been caught much earlier, treated much more easily, and with significantly less long term effects.
I couldn't easily find studies on preventative care leading to better outcomes, but given how many diseases (like cancer for example) can go from easily treatable to a catastrophic nightmare depending on how early they are detected, I find it hard to believe that easy, cheap (or free) access screenings would have no effect on outcomes, though I realize how treacherous it can be to rely on instinct instead of data.