Answer
No, annotations cannot be created or edited in ArcGIS Pro. Furthermore, the Convert Annotation to Text function in ArcMap is not currently available in ArcGIS Pro.
Labels must be converted to geodatabase annotations using ArcMap and can only be displayed/viewed using ArcGIS Pro. When converting labels to annotations in ArcMap, ensure the annotations are saved to a database, not to a map document.
In some cases, when attempting to edit an annotation layer, the message Relationship query tables cannot be edited is displayed in the Editing Status dialog box.
Geodatabase annotation layers can be displayed in ArcGIS Pro, but is it not possible to create new annotations from these layers or from labels. Annotations are not editable in ArcGIS Pro, as the individual features of the labels are not movable. Linking the annotation to a feature class (in ArcMap) allows the annotation to be moved or rescaled in ArcGIS Pro with the feature, but the annotation cannot be edited, moved within, or resized independently from its feature.