No, the XY tolerance of a feature class is not recalculated when adding a feature class to a feature dataset, which both have the same spatial references, using the drag and drop method.
The drag and drop method moves an item, such as feature class, to another location. During the drag and drop process, no other actions like recalculation or transformation takes place. This is because tolerance is only editable during the creation of a feature class and cannot be altered once the feature class is created. However, when a feature class is dragged and dropped in a dataset, the feature class is not created, but just moved from one location to another. The data is projected to a coordinate system, but a datum transformation is not performed.
The appropriate methods to move the data are the copy/paste method, which uses the data transfer tool, or the Import option, which uses Feature Class to Feature class tool. Both methods create a feature class, which enables the software to alter XY tolerance values.