It really depends on the word "excessive." Excessive training for anything by anyone can result in the body being unable to repair and remodel to keep up with the demands tearing it down or using up energy sources. It will not stop their bodies from growing, but they will require more food to compensate. In fact children who engage in physical activities on a regular basis will be well ahead of their peers in almost every category, including the smarts department. Plenty of studies have proven this.
Think of it this way - it isn't the activity itself, or even an abundance of it that stunts growth, it is a lack of nutrition coupled with incorrect programming of the activity. After studying athletes the world over (female gymnasts are a great example of this), almost all athletes I've studied who were "stunted" were so because their nutrition needs were not met, along with improper programming of their training. Luckily this paradigm has changed over the years and you see stronger athletes with better nutrition.
Coaches and parents should be mindful to allow children to rest when necessary, and ensure adequate nutrition along with proper programming for training activities. Luckily swimming unlike land sports doesn't have the drastic jarring forces upon joints and bones, and very little risk for injury when properly supervised (drowning is always a risk which I'll touch on later).
In fact, swimming teaches them many of the things they should be focusing on for their age, namely balance and coordination. Along with aerobic and anaerobic fitness, swimming is a great "play workout" for children, and heck adults as well. While children won't get as much into the mindfullness that an adult will, proper technique learned early removes the need to retrain later on in life.
Additionally, one of the highest killers (ranked 5th overall by the CDC) is unintentional drowning (and is number 2 behind car crashes for kids ages 1-14). Swimming is a life skill which in my opinion should be emphasied for children (as a father of a 4 year old, my son is in the pool as much as possible practicing essentials such as floating and moving himself through the water).
You asked the time and I built a watch, but I hope this helps to answer the question and give some insight! Properly programmed training coupled with excellent nutrition will help any child advance.