The broken part is done for. I have problems when I separate my musa's and don't get enough roots. the part in the ground should continue to grow. I cut all of bananas off every year for winter and they grow back. even the one's I take in as insurance, I will cut them down to around 4ft. I would make sure that the break is clean and not jagged. If it's jagged I would cut it with a sharp knife at an angle. That will help new leaves from getting stuck and let the rain run off.