Yep--JetBlue is currenly flyingout of Terminal E in Boston (The International Terminal) until Delta finishes construction on thier new digs.
We flew with them last year, and did curbside checkin around (9:30 am or so) There was also checkin right inside the doors at the counter, so if curbside is not open that early, you do not have a very far walk.
I would reccommend getting there a bit earlier than 5:30, however, as there is kind of a weird set up to get from the checkin area out to the gates. There is a checkpoint after you go down the escalator, where the attendant just looks at ID and boarding passes, then you get to security (where there was only one station) so if there is any sort of crowd, you could get delayed pretty easily.
We found it very easy to get through, because I think we were travelling mid-morning out of the international terminal, so there was not a lot of traffice at that time. Mind you it was also way back in February, and with the constant state of construction Logan is under, this all could have changed.
BTW--you will LOVE jetblue, really nice experience with them!