Absolutely! The advantages go beyond music related matters, but first, let me list the music related ones:
 
When participating in music competition, there is a deadline towards which your child (and you!) would need to work towards and master the pieces. Without that deadline, it is much harder to complete learning of the pieces within a finite period of time.
 
When the child knows he will be playing not only in front of public, but in front of judges that will intently listen to him, it pushes them to do considerably better and make sure he doesn’t embarrass himself amongst musicians, peers and parents.
 
After participation in a competition, you will notice that your child’s playing quality and capability goes up a notch, since the whole experience pushes your child to do more and better.
 
In a competition your child, as well as you, can come across other children that may be a lot better than him; without exposure to others, one may think that your child is the most talented young player of the current century, which is a dangerous notion and will severely hamper your child’s advancement in music. By seeing others, you and your child will realize qualities that many other children have, learn from them and aspire towards working harder to do better.
 
Other advantages gained that go beyond music are:
 
Participating in competitions enhances the competitiveness in your child, which is a quality that will be valuable for your child’s future both in their music activity and their careers.
 
During competitions, children get to know each other and have a chance to socialize and create long term relationship. After all, they share a common interest, which is the passion for music. They also learn to be respectful towards their competitors and be humble.
 
Your child doesn’t need to win the first prize to be proud about her accomplishments. Being in top 5 (even top 20 if a large competition!) of a category is a good enough reason for your child and you to be proud of having accomplished something significant. There are some superb interprets, such as Alfred Brendel, that have never won a prize in any competition, yet he is one of the most admired pianists of our time. In fact, in my opinion, if your child wins the first prize all the time is not the best thing that could happen to him, because he may come to the wrong conclusion that there is no other player better than him, which is not right in the case of any player.