You have to have a minimum to start, but lots of kids become better athletes, (bigger, stronger, faster, quicker, more explosive, better leapers) just through today's training.
My son and I just had a recruiting meeting with the Georgetown soccer coach. He told us that this spring his guys improved their vertical jump as much as 4 inches (2" on average) just from the training they did.
There are certainly individual limits based upon DNA, body type, etc., but you can certainly become a better athlete.