Does App info transfer from one device to another?

So if I have a smartphone and make a lot of annotations that are saved on that phone, then I upgrade to a new phone or if I want to access that information on a tablet, is this possible?

The Gospel Library application stores your data on church servers. However, that data is not stored there unless you synch annotations. There are other threads discussing issues with annotations and highlighting not appearing the same from one device to the next and with LDS.org.