Yes you can definitely download the LM data as a single file. You can find the path to the listmode data (file usually located somewhere like JHUNIG/OILKJU/RTHERT/LIST0000.BLF) in the DICOM header if you browse from the scanner.
Be aware that to process this outside of the scanner environment, you'll need some dedicated software with a lot of GE specific information on how to interpret the file (and also the calibration files) to be able to actually reconstruct any images. Its probably best to do these reconstructions on the scanner if you can!