Not without a custom plugin that tracks which tags were associated with posts in a particular category. This could be done via the term_group field in the wp_terms database table. I guess that the category ID could be used for the term_group.
When a post is published, the term_group could be set to the category ID for all the associated tags.
Maybe a plugin for this is already available?
Anyway, what do you want to display? A Tag cloud in a category archive????????