I imagine the monitor provides its own 5V supply for the USB ports, so does the drive also work on a single port?
Probably. I'd prefer to keep the cable and the drive together, though. Otherwise I'll forget what the cable's for and then I'll find myself unable to use the drive with something that doesn't provide enough juice (such as my Surface Go).
I find myself using an external drive because I simply no longer have a PC with an accessible 5.25" drive bay, in case you were wondering.