As far as I know this is not possible for feature classes, which ArcCatalog displays. Feature classes exist in ArcCatlog independent of all layers and have no query bulding capabilities. Desktop never displays a feaure class directly like ArcCatalog does and always display feature classes as feature layers only. Only feature layers have query builder functionality. I think this would only be possible within ArcCatalog through a saved layer file created by Desktop.
So similiar in an ArcMap session where you add feature classes in your table of conents and you have the option to build a query to filter features (or records if it's a table). Same functionality would be nice in (ArcCatalog within the Preview tab).
Filtering features in a feature class or filtering rows in a table using a definition query is only possible when data is added to a map. The definition query is a property of the map layer, and is not available as a property of the feature class or table. For example, when you open the Properties dialog box for a feature class or a table, there is no option available to define a definition query.
This is true for both ArcCatalog and ArcGIS Pro. When you preview data in either ArcCatalog or in a Catalog view in ArcGIS Pro, you can preview the data directly as a precursor to using the data for analysis or visualizing the data in a map to know you will be working with the correct dataset. The place to define properties of a map or table layer is in the map itself, in both ArcMap and in ArcGIS Pro.
