No. It is not possible to convert a stand alone annotation feature class into a feature linked annotation feature class.
The main difference between stand alone annotation and feature linked annotation is that a stand alone annotation feature class does not have a default text symbol, and it does not have an expression.
Simply creating a relationship class between the stand alone annotation feature class and another feature class is not enough to create proper feature linked annotation. Creating this properly requires manipulating properties of the annotation class in manners not possible using the ArcCatalog or ArcMap interface.