Is it possible to remove the automatically created Validation Status field when running a batch attribute rule in ArcGIS Pro?

No, it is not possible to remove the Validation Status field from an attribute table when running a batch attribute rule in ArcGIS Pro.

As a workaround, to remove the Validation Status field, export the feature class and remove the Validation Status field from the new feature class containing the original feature class attributes.

1. Create a new file geodatabase to store a new feature class. Refer to ArcGIS Pro: From the Catalog pane in ArcGIS Pro for instructions.

Note:
A new file geodatabase is useful to store the feature class without the Validation Status field while retaining the field for the feature class stored in the original geodatabase.

2. Navigate to the Analysis tab and click Tools. The Geoprocessing pane opens.
3. In the Geoprocessing pane, search for and select the Export Features tool.

Note:
Alternatively, the Feature Class To Feature Class tool can be used for this workaround but the tool is deprecated and is to be removed in a future release.

4. On the Export Features pane, configure the parameters of the tool.
   1. For Input Features, click the drop-down menu and select the feature class with the Validation Status field. In this example, the feature class named County is selected.
   2. For Output Feature Class, click Browse . Browse to the newly created file geodatabase in Step 1 and select it to store the output feature class.
   3. Scroll down, and click Fields to expand the list of the fields in the feature class.
   4. Under Field Map, under Output Fields, browse and select the VALIDATIONSTATUS field. Click the Remove icon displayed beside the VALIDATIONSTATUS field.
   5. Leave all the other parameters as default. Click Run.