There's a lot of factors at play here - it depends on a lot of things. In general, though, I think that this is more true the longer the target race is: the best thing to do in order to improve is to run as high mileage as the body is capable of doing without getting injured. Obviously everyone's different - not everyone can handle high mileage, but high mileage will never hurt anyone if the body can handle it - I would probably even claim that it can only improve someone.
For me personally, I was basically a 5:20 miler, 20:00 5k-er, 1:35 half marathoner, on an average of 30-35 mpw and a high of 40 or so, for the first 4 years of my running. After going up to 45-50 mpw average, I became about 5:10/19:00/1:32. In the sixth year, after training for a marathon and averaging probably 60mpw for that (and running a 3:20 marathon), I further improved to around 18:30 for 5k and 31:00 for 8k. In the seventh year, I was inconsistently running, lower mileage, but in that year, with minimal speed training, I ran a 5:05 mile and in addition, lowered my half-marathon time to 1:25 - huge improvement there. In my 8th year, I made drastic improvements to 17:15 for 5k and 28:20 for 8k, and later in that year I lowered my HM time to 1:24 (not going all out) and ran a 3:01 marathon 2 weeks later on a 90mpw avg plan. I am finishing up my 9th year of running now, and in this year, although it was not 12 full months of running, I lowered my mile to 4:59, 5k to 17:01, and marathon to 2:58:48.
All that is to say, my first four years I was basically stagnating. True, I probably wasn't training how I should have been, but I did not PR after my first year of running, through the fourth year, all of those years being the same mileage. I never improved until I increased my mileage - that is, until I began training for marathons! Obviously, this is anecdotal, but I am nearly positive this could happen to many people.
Obviously, you have to be smart about it - you don't have to constantly run 90 mpw in order to improve, but if your body can handle it, more mileage at least for a base training period will only make you stronger. It will increase your ability to do well at quality. I think quality can be improved by running quantity - some can do both at once. OK, I'm done.