Depends on the adapter and whether there's a Linux driver for it.
I managed to get an ASUS AC-56R USB adapater working over a year ago, but only after doing some extensive research and finding out that the instruction set that comes with the adapter had been totally borked for over a year, and ASUS had yet to fix it. Ended up downloading a fix from git that was developed by another user. Worked OK, but wasn't too stable and I ended up taking it back after a day of use.
Not all USB Wireless adapters have a Linux driver. Do your research before purchasing one.