Hi Ross,
According to Workfront's API Explorer, the reservedTime (Time Off) object does not have an "entryDate" field and based off a quick review of the updates feed in the setup area, it doesn't appear that you are able to track time off records within the updates feed.
You can certainly create a Time Off report to display time off records entered by users on their profile but otherwise, the functionality is quite limited at the moment. Of course, you can use Workfront Fusion and other iPaaS products to gather time off data and store it in external databases so that reporting tools like PowerBI and Tableau to create advanced reports based on the data collected from Workfront.