My HP Power supply has a button on the top that turns of the charging and just supplies power to the laptop, it has a warning sticker that says 'Do not charge onboard aircraft'. This would support the notion that the power ports don't put out enough power to run and charge at the same time.

If anyones interested it is HP Part No. 394202-001

Also looking at the specs on the back;

Charge Mode Output - 19.5V 3.3A
Non-Charge Mode Output - 15V 4.3A