Yes, you can add additional fields to the feedback widget. Please navigate to Admin > Workflows > Ticket fields > add the required custom field > click on it to be taken to the field properties. 

Here, please check the boxes, 'display to customer' and 'customer can edit' to make it available on the feedback widget.

Now navigate to Admin > Channels > Widgets > Feedback Widget. In the General tab, under Form options, choose 'Show form with ticket fields'.