I'm afraid your answer is no.
EE does not make it's custom field types available outside of the Channels functionality and it would be a nice feature to have in other parts of the system such as for Members or some addons like ones that add form functionality.
This is why you see several addons such as Profile:Edit and Zoo Visitor actually create a relationship between the default Member functionality and the Channels, so that you can have more control over managing your users custom fields with the benefits of EE's custom field types.
I have not seen any similar solution for Categories.
Some unsatisfying options to consider:
- Add HTML directly to your Category fields. They may not have a Wysiwyg but they will accept HTML.
- Experiment with the "Default Text Formatting" setting which allows you to modify the output of the category fields with a plugin that you have installed
- Consider creating a channel and using a relationship field instead
Like I said, all unsatisfying!