I would think this is pretty obvious. I don't think it's a direct correlation as much as it feels like a side effect of said process.
An example would be you find a great candidate who is a great fit, and then they demonstrate this with a great technical interview. I would also think when you go through a tough interview and are successful, that candidate feels vindicated they have the chops to compete and succeed in a company with a lot of competition. A lot of these companies in my area are well known and the guys who work there like to say they work there - since it's like getting accepted into an Ivy League school, there's a sense of satisfaction with getting chosen to work there.
In my experience, I've had it go both ways.
One shop I had three interviews, a code challenge and a final interview with the IT director. Afterwards, I got the gig, and then they low balled my salary. It was a very hipster startup and well known among developers as a "cool, geeky" place to work. I was surprised at how they promoted all the perks, "All the Red Bull you can drink! Free video games! Beer:30 EVERY DAY!!" but failed to say how little their developers get paid. It was eye opening to say the least.
On the flip side, I've had "one-time" interviews where you get one shot to impress somebody and have been successful and loved the job and stayed there for many years.
