Yes and no. Are you asking specifically about the DominoCalendarJsonLegacyService or one of the other REST services?
The DominoCalendarJsonLegacyService was built as a custom/convenience service for the iNotes calendar control so it does filter by dates - a request typically looks like this:
http://server/db.nsf/calendar.xsp/inoteslegacyjson?startKey=20120129T000000%2C00Z&untilKey=20120204T000000%2C00Z
where the startKey and untilKey keys are read from the parameter map and used to create a daterange object, which is then used as a key filter on the backend calendar view.
Since the iNotes calendar has no built-in category features, it does not filter by category - I imagine the request you had in mind would be like this:
http://server/db.nsf/calendar.xsp/inoteslegacyjson?categoryFilter=finance
Of course it could be updated to handle this scenario. Bear in mind however that a lot of these filters are mutually exclusive - mixing date filters and category filters do not work together due to restrictions in the backend Java classes ... you cannot create a single view navigator based on keys and category filters.
You might want to experiment with the other REST services (besides DominoCalendarJsonLegacyService) also.