This can be done, but the potentially variable number of values that will increase as you add more types can cause a problem as check box and radio button formatted fields have a fixed size. If you set up a "use values from field" value list, you may end up with a field that can't display all the check boxes or radio buttons. There is, however, a way to handle that situation. I'll include a link to a special exploration file that includes demos of what looks like a check box field formatted with a scroll bar at the end of this post.
To answer your main question, yes, such a field (either the standard field of check boxes or the "scroll bar" version) can be used to either filter a found set of records or a related set of records displayed in a portal.
To use check box values to filter a found set, see the examples at the end of this thread: Scripted Find Examples
To filter a portal, this can be done without any scripting if you use the check box field as match field in the relationship. You can also reference the values in the field in a portal filter expression.
The download link that I promised: "Adventures in FileMaking #2 - Enhanced Value Selection".