Not yet automatically - but iCloud sharing is coming in a new release soon.
Because data is stored locally on your device, it cannot be accessed from another device. For example, if you have both an iPhone and an iPad connected to the same Apple ID, Clever Net Worth may get installed automatically on both devices when you first purchase it from one of them. However the two versions will act independently and not share data.
You could copy a data set from one device to another by using the Export and Import function (see here) but this is a manual and non-straight forward process.