Yes, you can extract applicants' approval dates using Timestamped Exports -- the export will show you the date and time stamps of when each applicant landed in each stage for the specified opening.
Timestamped Exports also provide numbers on how many applicants moved to each stage. To create a new Timestamped Export, simply click on 'Reports' at from the top menu icon and select Exports --> Timestamped Exports.
Once you add a new Timestamped Export with your desired parameters, you can download it at any time.
Please note that you'll likely need to manually manipulate the data inside the export to grab the information you're looking for.