On my car, the recommended inflation is between 36 and 39 if I recall well.
I had to inflate them a few weeks ago as they were very low (around 29 I think), and I was about to be involved in a crash. I had sun in my eyes and I was coming out of a roundabout and the car in front of me decided to stop (there was someone crossing). I had the sun in my eyes and I didn't see the brake lights (car was silver, so sun was reflecting a bit). Put my foot down on the brakes and stopped just in time.
I feel that if they were inflated, I would have hit the poor car in front of me!
In fact, after inflating them, I had to smash the brakes again. This time I didn't notice the pelican crossing turned orange (its a main road, where everyone is going 80 km/h, why would you do a pelican crossing there?!?!) and I smashed the brakes again. This time the stopping distance was MUCH longer (although I was going a bit faster). The tyres are inflated at around 42.
So yes, it makes a difference. And it can prevent a crash. Inflate them every 6 weeks, and keep within the range.