AA is pretty specific about the use of the in-seat power port.
http://www.aa.com/content/travelInfo...tml#Powerports
<font face="Verdana, Arial, Helvetica, sans-serif" size="2">Your seat may be equipped with a DC power outlet. American uses a "cigarette lighter" style outlet delivering 15 volts of direct current. On most aircraft*, a power outlet is available at each seat in First and Business class, as well as selected rows in the Coach cabin. Outlets may be used to operate laptop computers, CD/DVD players, charging cellphone and other devices. Outlets are located on your seat console, or mounted to the seat frame below your seat cushion. Look for the 'lightning bolt" symbol on the overhead bin rows containing powerport-equipped seats. For detailed powerport locations by aircraft type, visit the 'Our Planes' section on AA.com. This information can also be found in the AA Timetable. </font>
Inverters are not listed and given that you can draw more power through the inverter than actually provided by the port - it's not in the approved list.
Keep in mind that regulations are not "allowed unless prohibited". It's the reverse. All devices except those specifically allowed are prohibited.