Is it possible to add CSS to the user edit page?
This depends on which theme you are using for your admin theme. If you are using a custom theme for the admin theme, you can add CSS in that custom theme. Otherwise, this is possible in a custom module via hook_css_alter().  

Can you provide more information?


Are you using a contributed theme or sub-theme as the admin theme?
Which version of Drupal are you using?
Does the CSS only need to be loaded on the user edit page? What are you trying to change on the user edit page?


I highly recommend reviewing the Drupal documentation on theming: https://www.drupal.org/node/341246

Here are some similar questions:
How to Override CSS for a core module?
How to override some admin theme CSS rules?   

Good example solution: http://purewebmedia.biz/article/2014/04/23/adding-your-own-css-admin-theme