Is there a way to partially hide the tabs, and have them come up as people fill out the form?

If you're using the Form Tabs widget  in your form, then will not be possible to hide the tabs here with conditions, conditions can only handle fields in the form, hiding or showing them, widgets are also allowed in the show/hide conditions. 

If you only want to hide some fields based on other field's selections or input, please  check this guide for further details: https://www.jotform.com/help/316-How-to-Show-or-Hide-Fields-Base-on-User-s-Answer 

If you have any question, please let us know.