Based on the many times I used to be at a GameStop and saw how parents, mostly the mother, would buy violent games for their kids without ever looking at the rating, no, definitely no. I even remember advising parents not to buy certain games due to their rating and content, recommending something else that would be more appropriate. These days is still the same; I would say 2 out of 10, maybe just one follow the ESRB. Most parents think of video games as a virtual nanny, then cry wolf and blame video games when their kids do stupid shit or something terrible happens that catches the media's attention, like a shooting or some other similar incident.
I have a lot to say about this, but I've grown quite apathetic to the subject over the years to be perfectly honest.
Here's a recent anecdote: I was at the Walmart I frequent the most recently, and ended up eavesdropping on a few parents who were buying games for their children; they had the foggiest idea of what they were doing, so I did my best to help them. One that stands out was a couple who had picked Just Cause 3, Persona 5, and The Witcher 3 for their 11-year-old son, and I think at one point they picked God of War as well. The crux was that the mother kept going on about how she didn't want to get her son any violent games, yet held in her hands three 'M' rated video games that she seemed to strongly consider getting. I tried to just ignore the noise, but I had to intrude. She said she picked those games because the covers seemed "childish" (her words), and that she didn't pick Mortal Kombat XL and Bloodborne because one had "mortal" and the other "blood" on the title. And by that I assume they left God of War because it has "war" on the title. I think that says a lot, quite frankly.