No. One of ERNIT's core features is showing how close your child is to making its wish come true. 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 wishes 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 wish 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.