Do BA even recruit graduates who aren't on the FPP
Again, as the above person said - in theory, yes. But they will only take people that have not completed the AQC (the MCC/JOC course). This means that they would select you at some odd point during the training, which seems unlikely as for half of it you will be out in New Zealand. The only time I could really see them taking people on was either in groundschool or in the waiting period before the AQC starts (we waited about 6 weeks but can be longer, can be shorter of course!). This is a very narrow margin of availability so it is pretty unlikely. If you were perused by BA, there would be a supplement to the course cost (although I have no idea what that is anymore).
In short, NO. They haven't been for a long time and it is very unlikely. Your best bet would be to go and apply for the FPP and hope that you get in!