I have no idea whether or not Jet Blue has the laptop connectors. Few airlines do - I have found them on American Airlines. But, they are not always available even in business or first class on some airlines. If you have a spare battery and can last a long flight - you may not need it - but for watching DVD movies, etc., I is almost necessary to run on external power. The main thing is to have a working computer when you get to where you area going. In the last 3 years, I have only found computer connections on 2 out of 10 flights. But - I have the adapter just in case.
Suggest you ask Jet Blue if they have the connections available on your flight.