Query advantages of OctoPrint
I have read that if I disconnect OctoPrint when printing, the print will stop.

You can disconnect your computer from the OctoPrint server while printing and the print will continue just fine. You cannot disconnect the OctoPrint server from the printer without interrupting the print, of course.

Since I thought the advantage of OctoPrint over, say, printing from Cura, was that it didn't tie up the computer while the print was taking place, what are the advantages of OctoPrint?

The advantage (the one you're talking about, anyway) of printing via OctoPrint (which you can also do via Cura, btw) is that you don't have to tie up the computer that you're using for other things. You run OctoPrint on some other computer that can stay connected to the printer. Typically, a Raspberry Pi is used; they're cheap (~$30), and there's an OctoPi distribution that's practically a turnkey solution.
Other advantages of OctoPrint include:

stores your .stl files, either on the print server or on the printer's SD card
enables remote monitoring, including a webcam feed
lets you control your printer from any device with a web browser
provides a plugin mechanism (and a large variety of plugins) to extend its capabilities