Of course not crawling "makes a difference" in some children - in the minority of children who bottom shuffle, it is a sign of problems with co-ordination. Children with dyspraxia and almost all children with dyslexia have problems with co-ordination. Teaching such children to crawl will of course help them with their co-ordination, as it will teach them a new skill that requires communication between the left and right side of the brain, and increase their strength (low muscle tone is also quite common in dyspraxic children, so strengthening exercises are good to counteract this). It is therefore a good idea to teach a child KNOWN to have co-ordination difficulties to crawl at some point, as part of the long journey to help them learn the skills they need in everday life. Having done this, dyspraxic children will still need help learning to feed themselves neatly, dress themselves and write clearly - it won't cure them of their co-ordination problems, however young they are when you teach them. And there is not enough evidence to prove it will help them with anything else whatsoever(eg reading, attention, perception, concentration or IQ).
My son didn't roll over, get from lying to sitting, sitting to standing, bottom shuffle or crawl until he started physiotherapy at 15 months. At 17 months he could bottom shuffle, at 19 months he could crawl and at 23 months he could walk. Does he have any problems with his co-ordination, attention, perception, concentration or reading now, at age 4? Not so far as I can see - he can read fluently, write clearly, has the most amazing memory and concentration, and shows no signs whatsoever of having perceptual problems (and was clearly afraid of heights long before he could crawl...). All in all, he's amazingly advanced (and I really don't think that's because we had to teach him to crawl!!!). He's still got low muscle tone, hypermobility and rather weak muscles, though, so I suspect there is a physical cause to that, rather than a brain-based one. But he's proof so far as I'm concerned that not learning to crawl at the "appropriate" time does not damage or limit the potential of a normal brain.