I tried it out on my last trip just for an experiment. The rail link from the airport to Phayathai is no problem - the train is clean & spacious and it's a much more interesting view than travelleing by taxi.
Phayathai to Sukhumvit on the sky train can be a pain in the arse if you have luggage (which I have). Not too bad if you are travelling outside peak periods but no fun if you're travelling when it's congested. Also note that the journey involves carrying your luggage up a few staircases - not a problem for me but maybe a problem for the more physically challenged mongers :P
Overall, I would use the rail link again outside peak periods and I would defintely use it if the traffic in Bangkok is grid locked. Other than that, I'll stick to using the taxi. :)