No... Currently Seattle is not part of Cathay Pacific network... And neither do they code-share with American Airways from San Francisco/Los Angeles to Seattle... But Cathay Pacific did operate flights to Seattle around 10 years ago as well as United Airlines... But sadly both of which have cut their operation to Seattle...
If you are wanting to travel to Seattle, you will have to fly via either Taipei or Tokyo as there is currently no direct air link between the two cities...
In my opinion, the best and quickest solution would be to fly with either China Airlines or EVA Air via Taipei as both of them do fly to Seattle... (China Airlines 3 Weekly Taipei-Seattle, EVA Air Daily Taipei-Seattle)...
Other option include flying Northwest Airlines/United Airlines via Tokyo...