Anything you pull off the powerchair counts as medical equipment so do not count towards your baggage limit (carryon or checked). If you put it into a bag that has non-medical equipment (even if it's just a normal sock), it no longer counts as being only medical equipment so would count towards the limits.
I haven't flown Jet Blue with a powerchair, but I have with a manual chair several times. Things to be aware: The first few rows are a higher price and have a bit extra room. They may seat you in those for their own convenience, but don't count on it so if you want the extra room, pay for the upgrade (I believe you can add this on after you book the flights). I don't know how much it is, but it may be something to consider.