Are you kidding? What would you do for 15 hours at BKK airport?
Yes, of course you should go down town BKK, in particular if you have never been to BKK before. Go sightseing (various temples, Grand Palace, etc), take a trip on the Chao Phraya river, get a nice massage at Health Land + enjoy some great Thai food - there are plenty of things to do for a first time visitor.
It is very easy to get from/to the airport. You can take the city line (train) from airport to Phaya Thai St. (45 Bath) and then BTS or taxi from there. If you are two persons or more, take a taxi from the airport. Taxi in BKK is cheap. Fom airport to downtown maximum 400 THB + highway tolls. Both will take around 30 minutes although a taxi may take longer due to trafic congestion.
Enjoy!