No. One of ERNIT's core features is showing your child's goal and how close he or she is to reaching it. This gets tricky if the piggy bank is shared - but it definitely is possible to get around.
Also, the fact that the money is received at first and then to be distributed to your child's goals afterwards is to be considered. This is difficult to control if the children get different deposits on different occasions.
Think of ERNIT as a new version of the classic piggy bank you already know. It's only possible to share one between multiple children if they aim for a collective goal and get the exact same deposits of money. The same basically goes for ERNIT.
It is possible to connect one child per piggy bank. So if you have more children they need to have one piggy bank each.