Hi Chris,
Yes you can. If you have added a new field to a standard table using TableExtension, it will be able to use in 'DataItemTableView'.

However I agree with Zhu as it cannot be used in ReportExtensions and to overcome from it you can Copy and create a new report with same code lines and continue as it will then allow you to Customize the 'DataItemTableView' as it is a Customized Report copied from a standard report.
Thanks
Please do verify if this helps you.